Abstract
Regular Ring - A regular ring (in the sense of von Neumann) admitting an involutory anti-automorphism α→α* such that αα =0 implies α=0. An idempotent e of a *-regular ring is called a projector if e* =e. Every left (right) ideal of a *-regular ring is generated by a unique projector. One can thus speak of the lattice of projectors of a *-regular ring. If this lattice is complete, then it is a continuous geometry. A complemented modular lattice (cf. also Lattice with complements) having a homogeneous basis a 1 ..., a n , where n≥4, is an ortho-complemented lattice if and only if it is isomorphic to the lattice of projectors of some *-regular ring.
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References
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Borovkov, A.A.: Wahrscheinlichkeitstheorie, Birkhäuser, 1976 (translated from the Russian).
Borovkov, A.A.: Stochastic processes in queueing theory, Springer, 1976 (translated from the Russian).
Korolyuk, V.S. and Borouvskikh, Yu. V.: Analytic problems in the asymptotics of probability distributions, Kishinev, 1981 (in Russian).
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Spitzer, F.: Principles of random walk, v. Nostrand, 1964.
Barber, M.N. and Ninham, B.W.: Random and restricted walks, theory and applications, Gordon & Breach, 1970.
Chung, K.L.: Markov chains with stationary transition probabilities, Springer, 1960.
Gut, A.: Stopped random walks. Limit theorems and applications, Springer, 1988.
Kemeny, J.G., Snell, J.L. and Knapp, A.W.: Denumerable Markov chains, Springer, 1976.
Kemperman, J.H.B.: The passage problem for a stationary Markov chain, Univ. of Chicago Press, 1961.
Levy, P.: Processus stochastiques et mouvement Brownien, Gauthier-Villars, 1965.
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Revuz, D.: Markov chains, North-Holland, 1975.
Čentsov, N.N. [N.N. Chentsov]: Statistical decision rules and optimal inference, Amer. Math. Soc., 1982 (translated from the Russian).
Berger, J.O.: Statistical decision theory and Bayesian analysis, Springer, 1985.
Lehmann, E.L.: Testing statistical hypotheses, Wiley, 1988.
Häzjek, J. and Sidäk, Z.: Theory of rank tests, Acad. Press, 1967.
Lehmann, E.L.: Testing statistical hypotheses, Wiley, 1986.
Waerden, B.L. van der: Mathematische Statistik, Springer, 1957.
Bol’shev, L.N. and Smirnov, N.V.: Tables of mathematical statistics, Libr. of mathematical tables, 46, Nauka, Moscow, 1983 (in Russian). Processed by L.S. Bark and E.S. Kedrova.
Owen, D.B.: Handbook of statistical tables, Addison-Wesley, 1962.
Cohn, P.M.: Algebra, 1-3, Wiley, 1988.
Bourbaki, N.: Elements of mathematics. Algebra I, Addison-Wesley, 1974, Chapt. II (translated from the French).
Kurosh, A.G.: The theory of groups, 1-2, Chelsea, 1955-1956 (translated from the Russian).
Jacobson, N.: Lie algebras, Interscience, 1962.
Serre, J.-P.: Lie algebras and Lie groups, Benjamin, 1965 (translated from the French).
Chevalley, C.: Théorie des groupes de Lie, 3, Hermann, 1955.
Humphreys, J.E.: Introduction to Lie algebras and representation theory, Springer, 1972.
Bourbaki, N.: Eléments de mathématique. Groupes et algèbres de Lie, Hermann, 1975, Chapt. 7.
Carter, R.W.: Simple groups of Lie type, Wiley, 1972.
Varadarajan, V.S.: Lie groups, Lie algebras, and their representations, Prentice-Hall, 1974.
Knapp, A.W.: Representation theory of semisimple groups, Princeton Univ. Press, 1986.
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Milnor, J.: Introduction to algebraic K-theory, Princeton Univ. Press, 1971.
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Latysheva, K. Ya., Tereshchenko, N.I. and Orel, G.S.: Normally regular solutions and their applications, Kiev, 1974 (in Russian).
Coddington, E.A. and Levinson, N.: Theory of ordinary differential equations, McGraw-Hill, 1955.
Kamke, E.: Handbuch der gewöhnliche Differentialgleichungen, Chelsea, reprint, 1947.
Wasow, W.: Asymptotic expansions for ordinary differential equations, Interscience, 1965.
Hille, E.: Lectures on ordinary differential equations, Addison-Wesley, 1969.
Häjek, J. and Sidák, Z.: Theory of rank tests, Acad. Press, 1967.
Kendall, M.G.: Rank correlation methods, Griffin, 1970.
Hàjek, J. and Sidák, Z.: Theory of rank tests, Acad. Press, 1967.
Lehmann, E.L.: Testing statistical hypotheses, Wiley, 1986.
Hoeffding, W.: ‘‘Optimum’ nonparametric tests’, in Proc. 2nd Berkeley Symp. Math. Stat. Probab. 1950, Univ. Calif. Press, 1951, pp. 83-92.
Hájek, J. and Sidäk, Z.: Theory of rank tests, Acad. Press, 1967.
Tarasenko, F.P.: Non-parametric statistics, Tomsk, 1976 (in Russian).
Kolmogorov, A.N.: ‘Unbiased estimates’, Izv. Akad. Nauk SSSR Ser. Mat 14, no. 4 (1950), 303–326 (in Russian).
Rao, C.R.: Linear statistical inference and its applications, Wiley, 1965.
Waerden, B.L. van der: Mathematische Statistik, Springer, 1957.
Blackwell, D.: ‘Conditional expectation and unbiased sequential estimation’, Ann. Math. Stat. 18 (1947), 105–110.
Cramér, H.: Mathematical methods of statistics, Princeton Univ. Press, 1946.
Waerden, B.L. van der: Mathematische Statistik, Springer, 1957.
Bol’shev, L.N.: ‘A refinement of the Cramér-Rao inequality’, Theory Probab. Appl. 6 (1961), 295–301. (Teor. Veryatnost. Primenen. 6, no. 3 (1961), 319-326)
Bhattacharyya, A.: ‘On some analogues of the amount of information and their uses in statistical estimation, Chapt. I’, Sankhyā 8, no. 1 (1946), 1–14.
Bhattacharyya, A.: ‘On some analogues of the amount of information and their uses in statistical estimation, Chapt. II-III’, Sankhyā 8, no. 3 (1947), 201–218.
Bhattacharyya, A.: ‘On some analogues of the amount of information and their uses in statistical estimation, Chapt. IV’, Sankhyā 8, no. 4 (1948), 315–328.
Lehmann, E.L.: Theory of point estimation, Wiley, 1983.
Bakhvalov, N.S.: Numerical methods: analysis, algebra, ordinary differential equations, Mir, 1977 (translated from the Russian).
Marchuk, G.I.: Methods of numerical mathematics, Springer, 1982 (translated from the Russian).
Samarskiĭ, A.A. and Nikolaev, E.S.: Numerical methods for grid equations, 1-2, Birkhäuser, 1989 (translated from the Russian).
Hageman, L.A. and Young, D.M.: Applied iterative methods, Acad. Press, 1981.
Traub, J.F.: Iterative methods for the solution of equations, Prentice-Hall, 1964.
Fulton, W.: Algebraic curves, Benjamin, 1969.
Shafarevich, I.R.: Basic algebraic geometry, Springer, 1977 (translated from the Russian).
Priwalow, I.I. [I.I. Privalov]: Einführung in die Funktionentheorie, 1-3, Teubner, 1958-1959 (translated from the Russian).
Kurosh, A.G.: Higher algebra, Mir, 1972 (translated from the Russian).
Conway, J.B.: Functions of one complex variable, Springer, 1973.
Lang, S.: Algebra, Addison-Wesley, 1984.
Shafarevich, I.R.: Basic algebraic geometry, Springer, 1977 (translated from the Russian).
Quillen, D.: ‘Rational homotopy theory’, Ann. of Math. 90 (1969), 209–295.
Sullivan, D.: ‘Infinitesimal computations in topology’, Publ. Math. IHES 47 (1977), 269–332.
Chen, K.-T.: ‘Iterated path integrals’, Bulletin Amer. Math. Soc. 83 (1977), 831–879.
Morgan, J.W. and Griffiths, P.A.: Rational homotopy theory and differential forms, Birkhäuser, 1981.
Shafarevich, I.R.: Basic algebraic geometry, Springer, 1977 (translated from the Russian).
Hironaka, H.: ‘Resolution of singularities of an algebraic variety over a field of characteristic zero I’, Ann. of Math. 79, no. 1-2 (1964), 109–326.
Borevich, Z.I. and Shafarevich, I.R.: Number theory, Acad. Press, 1987 (translated from the Russian).
Pisot, C. and Zamansky, M.: Mathématiques générales: algèbre-analyse, Dunod, 1966.
Hardy, G.H. and Wright, E.M.: An introduction to the theory of numbers, Oxford Univ. Press, 1979.
Bachman, G.: Introduction to p-adic numbers and valuation theory, Acad. Press, 1964.
Waerden, B.L. van der: Algebra, 2, Springer, 1967 (translated from the German).
Borel, A.: Linear algebraic groups, Benjamin, 1969.
Borel, A.: ‘Linear representations of semi-simple algebraic groups’, in R. Hartshorne (ed.): Algebraic Geometry (Arcata, 1974), Proc. Symp. Pure Math., Vol. 29, Amer. Math. Soc., 1975, pp. 421-440.
Humphreys, J.E.: Linear algebraic groups, Springer, 1975.
Borel, A., et al. (eds.): Seminar on algebraic groups and related finite groups, Lecture notes in math., 131, Springer, 1970.
Steinberg, R.: Lectures on Cheyalley groups, Yale Univ. Press, 1968.
Steinberg, R.: ‘Representations of algebraic groups’, Nagoya Math. J. 22 (1963), 33–56.
Hochschild, G.: The structure of Lie groups, Holden Day, 1965.
Humphreys, J.E.: Introduction to Lie algebras and representation theory, Springer, 1972.
Jantzen, J.C.: Representations of algebraic groups, Acad. Press, 1987.
Artin, M.: ‘On isolated rational singularities of surfaces’, Amer. J. Math. 88 (1966), 129–136.
Artin, M.: ‘Algebraic construction of Brieskorn’s resolutions’, J. Algebra 29, no. 2 (1974), 330–348.
Brieskorn, E.: ‘Rationale Singularitäten komplexer Flächen’, Invent. Math. b (1968), 336-358.
Elkik, R.: ‘Singularités rationelles et déformations’, Invent. Math. 47 (1978), 139–147.
Kempf, G.: ‘Cohomology and convexity’, in G. Kempf, et al. (ed.): Toroidal Embeddings I, Lecture notes in math., Vol. 339, Springer, 1973, pp. 41-52.
Klein, F.: Lectures on the icosahedron and the solution of equations of the fifth degree, Dover, reprint, 1956 (translated from the German).
Laufer, H.B.: ‘On rational singularities’, Amer. J. Math. 94 (1972), 597–608.
Reid, M.: ‘Canonical 3-folds’, J. Geom. Alg Angers (1980), 273-310.
Slodowy, P.J.: Simple singularities and simple algebraic groups, Lecture notes in math., 815, Springer, 1980.
Wahl, J.M.: ‘Simultaneous resolution of rational singularities’, Compos. Math. 38 (1979), 43–54.
Tyurina, G.N.: ‘On the tautness of rationally contractible curves on a surface’, Math. USSR Izv. 2 (1968), 907–934. (Izv. Akad. Nauk SSSR. Ser. Mat. 32 (1968), 943-970)
Demazure, M., Pinkham, H. and Teissier, B. (eds.): Sém. singularités des surfaces, Lecture notes in math., 777, Springer, 1980.
Durfee, A.: ‘Fifteen characterizations of rational double points and simple critical points’, Ens. Math. 25 (1979), 131–163.
Shafarevich, I.R.: ‘Algebraic surfaces’, Proc. Steklov Inst. Math. 75 (1967). (Trudy Mat. Inst. Steklov. 75 (1965))
Iskovssiĭ, V.A.: ‘Anticanonical models of three-dimensional algebraic varieties’, in Current Problems of Mathematics, Vol. 12, Moscow, 1979, pp. 59-157; 239 (in Russian).
Hartshorne, R.: Algebraic geometry, Springer, 1977. Viktor S. Kulikov
Beauville, A.:’ surfaces algébriques complexes’, Astérisque 54(1978).
Semple, J. and Roth, L.: Introduction to algebraic geometry, Oxford Univ. Press, 1985.
Shafarevich, I.R.: Basic algebraic geometry, Springer, 1977 (translated from the Russian).
Beauville, A., Colliot-Hélène, J.-L., Sansuc, J.J. and Swinnerton-Dyer, P.: ‘Variétés stablement rationelles nonrationelles’, Ann. of Math. 121 (1985), 283–318.
Chevalley, C.: ‘On algebraic group varieties’, J. Math. Soc. Japan 6, no. 3/4 (1954), 303–324.
Demazure, M. and Grothendieck, A.: Schémas en groupes II, Lecture notes in math., 152, Springer, 1970.
Rosenlicht, M.: ‘Some rationality questions on algebraic groups’, Ann. Mat. Pura Appl. 43 (1957), 25–50.
Borel, A.: Linear algebraic groups, Benjamin, 1969.
Voskresenskiĭ, V.E.: Algebraic tori, Moscow, 1977 (in Russian).
Platonov, V.P.: ‘Reduced K-theory and approximation in algebraic groups’, Proc. Steklov Inst. Math. 142 (1976), 213–224. (Trudy Mat. Inst. Steklov. 142 (1976), 198-207)
Platonov, V.P.: ‘Birational properties of the reduced Whitehead group’, Dokl. Akad. Nauk BSSR 21, no. 3 (1977), 197–198 (in Russian).
Platonov, V.P.: ‘On the problem of rationality of spinor varieties’, Soviet Math. Dokl. 20, no. 5 (1979), 1027–1031. (Dokl. Akad. Nauk SSSR 248, no. 3 (1979), 524-527)
Platonov, V.P.: ‘Birational properties of spinor varieties’, Proc. Steklov Inst. Math. 157 (1981), 173–182. (Trudy Mat. Inst. Steklov. 157 (1981), 161-169)
Serre, J.-P.: Cohomologie Galoisienne, Springer, 1964.
Chernousov, V.I.: ‘On the rationality of spinor varieties over the rational number field’, Dokl. Akad. Nauk BSSR 25, no. 4 (1981), 293–296 (in Russian). English abstract.
Yanchevskiĭ, V.I.: ‘Reduced K-theory. Applications to algebraic groups’, Math. USSR Sb. 38, no. 4 (1981), 533–548. (Mat. Sb. 110, no. 4 (1979), 579-596).
Coxeter, H.S.M.: Introduction to geometry, Wiley, 1969, p. 178.
Cassels, J.W.S.: An introduction to the geometry of numbers, Springer, 1959.
Gruber, P.M. and Lekkerkerker, C.G.: Geometry of numbers, North-Holland, 1987.
Hlawka, E.: ‘Das inhomogene Problem in der Geometrie der Zahlen’, in Proc. Internat. Congr. Math. Amsterdam, Vol. 3, 1954, pp. 20-27. (Also: Selecta, Springer 1990, 178-185.)
Dellacherie, C. and Meyer, P.A.: Probabilities and potential, C, North-Holland, 1988, Chapt. XII (translated from the French).
Getoor, R.K.: Markov processes: Ray processes and right processes, Lecture notes in math., 440, Springer, 1975.
Sharpe, M.J.: General theory of Markov processes, Acad. Press, 1988.
Babich, V.M. and Buldyrev, V.S.: Asymptotic methods in the diffraction of short waves, Moscow, 1972 (in Russian).
Babich, V.M., Buldyrev, V.S. and Molotkov, I.A.: A space-time ray method, Leningrad, 1985 (in Russian).
Hörmander, L.: The analysis of linear partial differential operators, 1-4, Springer, 1983-1985.
Whitham, G.B.: Linear and nonlinear waves, Wiley, 1974.
Borovikov, V.A. and Kinber, B.E.: Geometric diffraction theory, Moscow, 1978 (in Russian).
Felsen, L.B. and Marcuntz, N.: Radiation and scattering of waves, Prentice-Hall, 1973.
Kline, M. and Kay, I.W.: Electromagnetic theory and geometrical optics, Interscience, 1965.
Strutt, J.W. (Lord Rayleigh): Wave theory of light, Moscow-Leningrad, 1940 (in Russian; translated from the English).
Papoulis, A.: Probability, random variables and stochastic processes, McGraw-Hill, 1965.
Strutt, J.W. (Lord Rayleigh): Theory of sound, 1, Dover, reprint, 1945.
Cesari, L.: Asymptotic behavior and stability problems in ordinary differential equations, Springer, 1959. See also the to Liénard equation.
Stoker, J.J.: Nonlinear vibrations in mechanical and electrical systems, Interscience, 1950.
Fife, P.C.: Mathematical aspects of reacting and diffusing systems, Lecture notes in biomathematics, 28, Springer, 1979.
Henry, D.: Geometric theory of semilinear parabolic equations, Lecture notes in mathematics, 840, Springer, 1981.
Smoller, J.: Shock waves and reaction-diffusion equations, Springer, 1983.
Conley, C.: Isolated invariant sets and the Morse index, Amer. Math. Soc., 1978.
Kolmogorov, A.N., Petrovskiĭ, I.G. and Piskunov, N.S.: ‘A study of the diffusion equation with increase in the quantity of matter, and its application to a biological problem’, Byull. Moskov. Gos. Univ. 17 (1937), 1–72 (in Russian).
Aronson, D.G. and Weinberger, H.F.: ‘Multidimensional nonlinear diffusion arising in population genetics’, Adv. in Math. 30 (1978), 33–76.
Kanel’, Ya. L.: ‘On the stability of solutions of the Cauchy problem for the equations arising in combustion theory’, Mat. Sb. 59 (1962), 245–288 (in Russian).
Fife, P.C. and McLeod, J.B.: The approach of solutions of nonlinear diffusion equations to travelling front solutions’, Arch. Rational Mech. Anal. 65 (1977), 335–361.
Fife, P.C.: Dynamics of internal layers and diffusive interfaces, CBMS-NSF Reg. Conf. Ser. Appl. Math., 53, SIAM, 1988.
Aris, R.: The mathematical theory of diffusion and reaction in permeable catalysts, 1-2, Clarendon Press, 1975.
Buckmaster, J. and Ludford, G.S.S.: Theory of laminar flow, Cambridge Univ. Press, 1982.
Jones, C.: ‘Stability of the travelling wave solution of the FitzHugh-Nagumo system’, Trans. Amer. Math. Soc. 286 (1984), 431–469.
Alexander, J., Gardner, R. and Jones, C.: ‘A topological invariant arising in the stability analysis of travelling waves’, J. Reine Angew. Math. (To appear).
Nishiura, Y., Mimura, M., Ikeda, H. and Fujii, H.: ‘Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems’, SIAM J. Math. Anal. 21 (1990), 85–122.
Harnack, A.: ‘Ueber die Vieltheitigkeit der ebenen algebraischen Kurven’, Math. Ann. 10 (1876), 189–198.
Hilbert, D.: ‘Ueber die reellen Züge algebraischer Kurven’, Math. Amm. 38 (1891), 115–138.
Hilbert, D.: ‘Mathematische Probleme’, Arch. Math. Phys. 1 (1901), 213–237.
Petrovskiĭ, I.G.: ‘On the topology of real plane algebraic curves’, Ann. of Math. 39, no. 1 (1938), 189–209.
Oleĭnik, O.A. and Petrovskiĭ, I.G.: ‘On the topology of real algebraic surfaces’, Transl. Amer. Math. Soc. 7 (1952), 399–417. (Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 389-402)
Oleĭnik, O.A.: ‘On the topology of real algebraic curves on an algebraic surface’, Mat. Sb. 29 (1951), 133–156 (in Russian).
Hilbert problems, Moscow, 1969 (in Russian).
Arnol’d, V.I.: ‘Distribution of the ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms’, Funct. Anal. Appl. 5, no. 3 (1971), 169–176. (Funkts. Anal. 5, no. 3 (1971), 1-9)
Rokhlin, V.A.: ‘Congruences modulo 16 in Hilbert’s sixteenth problem’, Funct. Anal. Appl. 6, no. 4 (1972), 301–306. (Funkts. Anal. 6, no. 4 (1972), 58-64)
Rokhlin, V.A.: ‘Congruences modulo 16 in Hilbert’s sixteenth problem’, Funct. Anal. Appl. 7, no. 2 (1973), 163–165. (Funkts. Anal. 7, no. 2 (1973), 91-92)
Kharlamov, V.M.: ‘A generalized Petrovskiĭ inequality’, Funct. Anal. Appl. 8, no. 2 (1974), 132–137. (Funkts. Anal. 8, no. 2 (1974), 50-56)
Kharlamov, V.M.: ‘A generalized Petrovskiĭ inequality II’, Funct. Anal. Appl. 9, no. 3 (1975), 266–268. (Funkts. Anal. 9, no. 3 (1975), 93-94)
Kharlamov, V.M.: ‘Additive congruences for the Euler characteristic of real algebraic manifolds of even dimensions’, Funct. Anal. Appl. 9, no. 2 (1975), 134–141. (Funkts. Anal. 9, no. 2(1975), 51-60)
Kharlamov, V.M.: ‘The topological type of nonsingular surfaces in R P 3 of degree four’, Funct. Anal. Appl. 10, no. 4 (1976), 295–304. (Funkts. Anal. 10, no. 4 (1976), 55-68)
Gudkov, D.A.: ‘The topology of real projective algebraic varieties’, Russian Math. Surveys 29, no. 4 (1974), 1–80. (Uspekhi Mat. Nauk 29, no. 4 (1974), 3-79)
Sullivan, D.: Geometric topology, 1. Localization, periodicity, and Galois symmetry, M.I.T., 1971.
Viro, O.:’ successes of the last five years in the topology of real algebraic varieties’, in Proc. Internat. Congress Mathematicians, Warszawa 1983, PWN & North-Holland, 1984, pp. 603-619.
Wilson, G.: ‘Hilbert’s sixteenth problem1, Topology 17(1978), 53–74.
Tognoli, A.:’ some results in the theory of real analytic spaces’, in M. Jurchesan (ed.): Espaces Analytiques (Bucharest 1969), Acad. Roumanie, 1971, pp. 149-157.
Cartan, H.: ‘Variétés analytiques réelles et variétés analytiques complexes’, Bull. Soc. Math. France 85 (1957), 77–99.
Bruhat, F. and Cartan, H.: ‘Sur la structure des sousensembles analytiques réels’, C.R. Acad. Sci. Paris 244 (1957), 988–900.
Bruhat, F. and Cartan, H.: ‘Sur les composantes irréductibles d’un sous-ensemble’, C.R. Acad. Sci. Paris 244 (1957), 1123–1126.
Bruhat, F. and Whitney, H.: ‘Quelques propriétés fondamentales des ensembles analytiques-réels’, Comm. Math. Helv. 33 (1959), 132–160.
Narasimhan, R.: Introduction to the theory of analytic spaces, Lecture notes in math., 25, Springer, 1966.
Grauert, H. and Remmert, R.: Theory of Stein spaces, Springer, 1979 (translated from the German).
Dedekind, R.: Essays on the theory of numbers, Dover, reprint, 1963 (translated from the German).
Dantscher, V.: Vorlesungen über die Weierstrass’sche Theorie der irrationalen Zahlen, Teubner, 1908.
Cantor, G.: ‘Ueber die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen’, Math. Ann. 5 (1872), 123–130.
Nemytskiĭ, V.V., Sludskaya, M.I. and Cherkasov, A.N.: A course of mathematical analysis, I, Moscow, 1957.
Il’in, V.A. and Poznyak, E.G.: Fundamentals of mathematical analysis, 1-2, Mir, 1982 (translated from the Russian).
Kudryavtsev, L.D.: A course of mathematical analysis, 1, Moscow, 1988 (in Russian).
Nikol’skiĭ, S.M.: A course of mathematical analysis, 1-2, Mir, 1977 (translated from the Russian).
Fichtenholz, G.M.: Differential und Integralrechnung, 1, Deutsch. Verlag Wissenschaft., 1964.
Bourbaki, N.: General topology, Elements of mathematics, Addison-Wesley, 1966, Chapts. 3-4 (translated from the French).
Heath, T.L.: A history of Greek mathematics, Dover, reprint, 1981.
Heath, T.L.: The thirteen books of Euclid’s elements, 1-3, Dover, reprint, 1956.
Knorr, W.R.: The evolution of the Euclidean elements, Reidel, 1975.
Landau, E.: Foundations of analysis, Chelsea, reprint, 1951 (translated from the German).
Rudin, W.: Principles of mathematical analysis, McGraw-Hill, 1976.
Gericke, H.: Geschichte des Zahlbegriffs, B.I. Mannheim, 1970.
Kleene, S.C.: ‘On the interpretation of intuitionistic number theory’, J. Symbolic Logic 10 (1945), 109–124.
Kleene, S.C.: Introduction to metamathematics, North-Holland, 1951.
Kleene, S.C. and Vesley, R.E.: The foundations of intuitionistic mathematics: especially in relation to recursive functions, North-Holland, 1965.
Dragalin, A.G.: Mathematical intuitionism. Introduction to proof theory, Amer. Math. Soc, 1988 (translated from the Russian).
Hyland, J.M.E.: ‘The effective topos’, in A.S. Troelstra and D. van Dalen (eds.): The L.E.J. Brouwer Centenary Symposium, North-Holland, 1982, pp. 165-216.
Gauss, C.F.: Untersuchungen über höhere Arithmetik, Springer, 1889 (translated from the Latin).
Gauss, C.F.: ‘Theoria residuorum biquadraticorum’, in Werke, Vol. 2, K. Gesellschaft Wissensch. Göttingen, 1876, p. 65.
Eisenstein, G.: ‘Beweis des Reciprocitätssatzes für die cubischen Reste in der Theorie der aus dritten Würzein der Einheit zusammengesetzten complexen Zahlen’, J. Math. 27 (1844), 289–310.
Kummer, E.E.: ‘Allgemeine Reciprocitätsgesetze für beliebig hohe Potentzreste’, Ber. K. Akad. Wiss. Berlin (1850), 154-165.
Hilbert, D.: ‘Die Theorie der algebraischen Zahlkörper’, Jahresber. Deutsch. Math.-Verein 4 (1897), 175–546.
Hilbert, D.: ‘Ueber die theorie der relativquadratischen Zahlkörpern’, Jahresber. Deutsch. Math.-Verein 6, no. 1 (1899), 88–94.
Furtwängler, Ph.: ‘Die Reziprozitätsgesetze für Potenzreste mit Primzahlexponenten in algebraischen Zahlkörpern (Erster Teil)’, Math. Ann. 67 (1909), 1–31.
Furtwängler, Ph.: ‘Die Reziprozitätsgesetze für Potenzreste mit Primzahlexponenten in algebraischen Zahlkörpern (Zweiter Teil)’, Math. Ann. 72 (1912), 346–386.
Furtwängler, Ph.: ‘Die Reziprozitätsgesetze für Potenzreste mit Primzahlexponenten in algebraischen Zahlkörpern (Dritter und letzter Teil)’, Math. Ann. 74 (1913), 413–429.
Takagi, T.: ‘Ueber eine Theorie der relativ Abel’schen Zahlkörpers’, J. Coll. Sci. Tokyo 41, no. 9 (1920), 1–133.
Artin, E.: ‘Beweis des allgemeinen Reziprocitätsgesetzes’, Abh. Math. Sem. Univ. Hamburg 5 (1928), 353–363. (also: Collected Papers, Addison-Wesley, 1965, pp. 131-141).
Hasse, H.: ‘Die Struktur der R. Brauerschen Algebrenklassengruppe über einen algebraischer Zahlkörper’, Math. Ann. 107 (1933), 731–760.
Shafarevich, I.R.: ‘A general reciprocity law’, Uspekhi Mat. Nauk 3, no. 3 (1948), 165 (in Russian).
Lapin, A.I.: ‘A general law of dependence and a new foundation of class field theory’, lzv. Akad. Nauk SSSR Ser. Mat. 18 (1954), 335–378 (in Russian).
Cassels, J.W.S. and Fröhlich, A. (eds.): Algebraic number theory, Acad. Press, 1986.
Faddeev, D.K.: ‘On Hilbert’s ninth problem’, in Hilbert problems, Moscow, 1969, pp. 131-140 (in Russian).
Neukirch, J.: Class field theory, Springer, 1986.
Young, D.M. and Gregory, R.T.: A survey of numerical mathematics, Dover, reprint, 1988, p. 362ff.
Scheeffer, L.: ‘Allgemeine Untersuchungen über Rectification der Curven’, Acta Math. 5 (1885), 49–82.
Jordan, C.: Cours d’analyse, Gauthier-Villars, 1883.
Spivak, M.: A comprehensive introduction to differential geometry, 2, Publish or Perish, 1970.
Markushevich, A.I.: Rekursive Folgen, Deutsch. Verlag Wissenschaft., 1973 (translated from the Russian).
Feller, V.: An introduction to probability theory and its applications, 1, Wiley, 1968.
Bailey, N.T.J.: The elements of stochastic processes, Wiley, 1964.
Chung, K.L.: Markov chains with stationary transition probabilities, Springer, 1960.
Gihman, I.I. [I.I. Gikhman] and Skorokhod, A.V.: The theory of stochastic processes, I, Springer, 1974 (translated from the Russian).
Spitzer, V.: Principles of random walk, v. Nostrand, 1964.
Izobov, N.A.: ‘Linear systems of ordinary differential equations’, J. Soviet Math. 5 (1976), 46–96. (Itogi Nauk. i Tekhn. Mat. Anal. 12 (1974), 71-146)
Auslander, J. and Hahn, F.: ‘Point transitive flows, algebras of functions and the Bebutov system’, Fund. Math. 60 (1967), 117–137.
Birkhoff, G.D.: Dynamical systems, Amer. Mat. Soc, 1927.
Nemytskiĭ, V.V. and Stepanov, V.V.: Qualitative theory of differential equations, Princeton Univ. Press, 1960 (translated from the Russian).
Furstenberg, H.: Recurrence in ergodic theory and combinatorial number theory, Princeton Univ. Press, 1981.
Gottschalk, W.H. and Hedlund, G.A.: Topological dynamics, Amer. Math. Soc, 1955.
Sibirsky, K.S. [K.S. Sibirskiĭ]: Introduction to topological dynamics, Noordhoff, 1975 (translated from the Russian).
Peter, R.: Recursive functions, Acad. Press, 1967 (translated from the German).
Mal’tsev, A.I.: Algorithms and recursive functions, Wolters-Noordhoff, 1970 (translated from the Russian).
Uspenskiĭ, V.A.: Leçons sur les fonctions calculables, Hermann, 1966 (translated from the Russian).
Kleene, S.C.: Introduction to metamathematics, North-Holland, 1951.
Moschovakis, Y.N.: Elementary introduction on abstract structures, North-Holland, 1974.
Rogers, H., jr.: Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Peter, R.: Recursive functions, Acad. Press, 1967 (translated from the German).
Kleene, S.C.: Introduction to metamathematics, North-Holland, 1950, p. 234.
Odifreddi, P.: Classical recursion theory, North-Holland, 1989, Chapt. II; esp. pp. 199ff.
Rogers, jr., H.: Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Barwise, J.: Admissible sets and structures, Springer, 1975.
Rogers, jr., H.: Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Dekker, J.C.E. and Myhill, J.: ‘Recursive equivalence types’, Univ. California Publ. 3 (1960), 67–213.
Tierney, L.: ‘A space-efficient recursive procedure for estimating a quantile of an unknown distribution’, SIAM J. Scient. Statist. Comp. 4 (1983), 706–711.
Holst, U.: ‘Recursive estimation of quantiles using kernel density estimators’, Sequential Anal. 6 (1987), 219–237.
Robbins, H. and Monro, S.: ‘A stochastic approximation method’, Ann. Math. Stat. 22 (1951), 400–427.
Rousseeuw, P.J. and Bassett, G.W.: ‘The remedian: a robust averaging method for large data sets’, J. Amer. Statist. Assoc. 85 (1990), 97–104.
Pearl, J.: ‘A space-efficient on-line method of computing quantile estimators’, J. Algorithms 2 (1981), 164–177.
Mal’tsev, A.I.: Algorithms and recursive functions, Wolters-Noordhoff, 1970 (translated from the Russian).
Rogers, jr., H.: Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Everett, H.: ‘Recursive games’, in H.W. Kuhn, et al. (ed.): Contributions to the theory of games, Vol. 3, Princeton Univ. Press, 1957, pp. 47-87.
Alpern, S.: ‘Games with repeated decisions’, SIAM J. Control Optim. 26, no. 2 (1988), 468–477.
Mal’tsev, A.I.: ‘Constructive algebras I’. Russian Math. Surveys 16, no. 3 (1961), 77–129. (Also in: A.I. MaPcev, The metamathematics of algebraic systems, North-Holland, 1971, Chapt. 18). (Uspekhi Mat. Nauk 16, no. 3 (1962), 3-60)
Ershov, Yu. L.: Theory of enumerations, 3. Constructive models, Novosibirsk, 1974 (in Russian).
Ershov, Yu. L., Lavrov, I.A., Taimanov, A.D. and Taĭtslin, M.A.: ‘Elementary theories’, Russian Math. Surveys 20, no. 4 (1965), 35–105. (Uspekhi Mat. Nauk 20, no. 4 (1965), 37-108)
Goncharov, S.S.: ‘Selfstability, and computable families of constructivizations’, Algebra and Logic 14, no. 6 (1975), 392–408. (Algebra i Logika 14, no. 6 (1975), 647-680)
Nurtazin, A.T.: ‘Strong and weak constructivizations, and enumerable families’, Algebra and Logic 13, no. 3 (1974), 177–184. (Algebra i Logika 13, no. 3 (1974), 311-323)
Cobham, A.: Summaries of talks presented at the summer institute for symbolic logic Cornell University, 1957, Washington, 1960, pp. 391-395.
Fröhlich, A. and Shepherdson, J.C.: ‘Effective procedures in field theory’, Phil. Trans. Royal. Soc. London Ser. A. 2458 (1956), 407–428.
Mostowski, A.: ‘A formula with no recursively enumerable model’, Fund. Math. 42, no. 1 (1955), 125–140.
Rabin, M.O.: ‘Computable algebra, general theory and theory of computable fields’, Trans. Amer. Math. Soc. 95, no. 2 (1960), 341–360.
Vaught, R.L.: ‘Sentences true in all constructive models’, J. Symb. Logic 25, no. 1 (1960), 39–58.
Goncharov, S.S.: ‘Problem of the number of non-self-equivalent constructivizations’, Algebra and Logic 19, no. 6 (1980), 401–414. (Algebra i Logika 19, no. 6 (1980), 621-639)
Kleene, S.C.: ‘On the interpretation of intuitionistic number theory’, J. Symbolic Logic 10 (1945), 109–124.
Kleene, S.C.: Introduction to metamathematics, North-Holland, 1951.
Nelson, D.: ‘Recursive functions and intuitionistic number theory’, Trans. Amer. Math. Soc. 61 (1947), 307–368.
Rose, G.F.: ‘Propositional calculus and realizability’, Trans. Amer. Math. Soc. 75 (1953), 1–19.
Novikov, P.S.: Constructive mathematical logic from a classical point of view, Moscow, 1977 (in Russian).
Beeson, M.J.: Foundations of constructive mathematics, Springer, 1985.
Poorten, A.J. van der: ‘Some facts that should be better known, especially about rational functions’, in R.A. Molin (ed.): Number Theory and Applications, Kluwer, 1989, pp. 497-528.
Post, E.L.: ‘Recursively enumerable sets of positive integers and their decision problems’, Bull. Amer. Math. Soc. 50 (1944), 284–316.
Friedberg, R.M.: ‘Three theorems on recursive enumeration: I. Decomposition, II. Maximal set, III. Enumeration without duplication’, J. Symbolic Logic 23 (1958), 309–316.
Lachlan, A.H.: ‘On the lattice of recursively enumerable sets’, Trans. Amer. Math. Soc. 130, no. 1 (1968), 1–37.
Ershov, Yu. L.: ‘Hyperhypersimple m-degrees’, Algebra and Logic 8, no. 5 (1969), 298–315. (Algebra i Logika 8, no. 5 (1969), 523-552)
Degtev, A.N.: ‘Reducibilities of tabular type in the theory of algorithms’, Russian Math. Surveys 34, no. 3 (1979), 155–192. (Uspekhi Mat. Nauk 34, no. 3 (1979), 137-168)
Soare, R.J.: ‘Recursively enumerable sets and degrees’, Bull Amer. Math. Soc. 84, no. 6 (1978), 1149–1181.
Dekker, J.C.E. and Myhill, J.: ‘Recursive equivalence types’, Publ. Math. Univ. Calif. 3, no. 3 (1960), 67–213.
Mal’tsev, A.I.: Algorithms and recursive functions, Wolters-Noordhoff, 1970 (translated from the Russian).
Rogers, jr., H.: Theory of recursive functions and effective computability, McGraw-Hill, 1967.
Muchnik, A.A.: ‘On the unsolvability of the reducibility problem in the theory of algorithms’, Dokl. Akad. Nauk SSSR 108, no. 2 (1956), 194–197 (in Russian).
Soare, R.I.: Recursively enumerable sets and degrees, a study of computable functions and generated sets, Springer, 1987.
Barwise, J. (ed.): Handbook of mathematical logic, North-Holland, 1978.
Friedberg, R.M.: ‘Two recursively enumerable sets of incomparible degrees of unsolvability (solution of Post’s problem)’, Proc. Nat Acad. Sci. USA 43 (1957), 236–238.
Bass, H.: Algebraic K-theory, Benjamin, 1967, p. 152ff.
Hahn, A.J. and O’Meara, O.T.: The classical groups and K-theory, Springer, 1979, §2.2D.
Artin, M.: ‘Algebraic approximation of structures over complete local rings’, Publ Math. IHES 36 (1969), 23–58.
Grothendieck, A. and Dieudonné, J.: ‘Eléments de géométrie algebrique I. Le langage des schémas’, Publ. Math. IHES 4 (1960).
Mumford, D.: Lectures on curves on an algebraic surface, Princeton Univ. Press, 1966.
Oort, F.: ‘Algebraic group schemes in characteristic zero are reduced’, Invent. Math. 2 (1969), 79–80.
Harshorne, R.: Algebraic geometry, Springer, 1977.
Hilbert, D. and Ackerman, W.: Grundzüge der theoretischen Logik, Dover, reprint, 1946.
Russell, B. and Whitehead, A.N.: Principia mathematica, 1-3, Cambridge Univ. Press, 1925-1927.
Lyapunov, A.M.: Stability of motion, Acad. Press, 1966 (translated from the Russian).
Erugin, N.P.: ‘Reducible systems’, Trudy Mat. Inst. Steklov. 13 (1946) (in Russian).
Curtis, C.W. and Reiner, I.: Methods of representation theory, 1-2, Wiley (Interscience), 1981-1987.
Lichnerowicz, A.: Global theory of connections and holonomy groups, Noordhoff, 1976 (translated from the French).
Kobayashi, S. and Nomizu, K.: Foundations of differential geometry, 1, Wiley, 1963.
Wu, H.: ‘On the de Rham decomposition theorem’, Illinois J. Math. 8, no. 2(1964), 291–311.
Shapiro, Ya. L.: ‘Reducible Riemannain spaces and twosheeted structures on them’, Soviet Math. Dokl. 13, no. 5 (1972), 1345–1348. (Dokl. Akad. Nauk SSSR 206, no. 4 (1972))
Rham, G. de: ‘Sur la réductibilité d’un espace de Riemann’, Comm. Math. Helvetica 26 (1952), 328–344.
Springer, T.: Invariant theory, Lecture notes in math., 585, Springer, 1977.
Humphreys, J.E.: Linear algebraic groups, Springer, 1975.
Borel, A. and Tits, J.: ‘Groupes réductifs’, Publ. Math. IHES 27 (1965), 55–150.
Popov, V.L.: ‘Hilbert’s theorem on invariants’, Soviet Math. Dokl. 20, no. 6 (1979), 1318–1322. (Dokl. Akad. Nauk SSSR 249, no. 3(1979), 551-555)
Kobayashi, S. and Nomizu, K.: Foundations of differential geometry, 2, Wiley, 1969.
Rashevskiĭ, P.K.: ‘On the geometry of homogeneous spaces’, Trudy Sem. Vektor, i Tenzor. Anal. 9 (1952), 49–74.
Nomizu, K.: ‘Invariant affine connections on homogeneous spaces’, Amer. J. Math. 76, no. 1 (1954), 33–65.
Kantor, I.L.: ‘Transitive differential groups and invariant connections in homogeneous spaces’, Trudy Sem. Vektor, i Tenzor. Anal. 13 (1966), 310–398.
Vinberg, E.B.: ‘Invariant linear connections in a homogeneous space’, Trudy Moskov. Mat. Obshch. 9 (1960), 191–210 (in Russian).
Alekseevskiĭ, D.V.: ‘Maximally homogeneous G-structures and filtered Lie algebras’, Soviet Math. Dokl. 37, no. 2 (1988), 381–384. (Dokl. Akad. Nauk SSSR 299, no. 3 (1988), 521-526)
Wolff, J.: Spaces of constant curvature, McGraw-Hill, 1967.
Rees, D.: ‘On semi-groups’, Proc. Cambridge Philos. Soc. 36 (1940), 387–400.
Clifford, A.H. and Preston, G.B.: The algebraic theory of semigroups, 1-2, Amer. Math. Soc, 1961-1967.
Lyapin, E.S.: Semigroups, Amer. Math. Soc, 1974 (translated from the Russian).
Turchin, V.F.: ‘A meta-algorithmic language’, Kibernetika, no. 4 (1968), 45-54 (in Russian). English abstract.
Turchin, V.F. and Serdobol’skiĭ, V.I.: ‘The language REFAL and its use for transformation of algebraic expressions’, Kibernetika, no. 3 (1969), 58-62 (in Russian). English abstract.
Florentzev, S.N., Olyunin, V. Yu. and Turchin, V.F.: Proc. first all-union Conf. on programming, Kiev, 1968, pp. 114-133 (in Russian).
Romanenko, S.A. and Turchin, V.F.: Proc. second all-union Conf. on programming, Novosibirsk, 1970, pp. 31-42 (in Russian).
Budnit, A.P., et al.: Yadernaya Fizika 14 (1971), 304–313.
Levi-Civita, T. and Amaldi, U.: Lezioni di meccanica razionale, Zanichelli, 1949.
Arkhangel’skiĭ, A.V. and Ponomarev, V.I.: Fundamentals of general topology: problems and exercises, Reidel, 1984 (translated from the Russian).
Fleissner, W.G.: The normal Moore space conjecture and large cardinals’, in K. Kunen and J.E. Vaughan (eds.): Handbook of Set-Theoretic Topology, North-Holland, 1984, pp. 733-760.
Bourbaki, N.: Groupes et algèbres de Lie, Eléments de mathématiques, Hermann, 1968, Chapts. 4-6.
Vinberg, E.B.: ‘Discrete linear groups generated by reflections’, Math. USSR Izv. 35, no. 5 (1971), 1083–1119. (Izv. Akad. Nauk SSSR Ser. Mat. 35, no. 5 (1971), 1072-1112)
Gottschling, E.: ‘Reflections in bounded symmetric domains’, Comm. Pure Appl. Math. 22 (1969), 693–714.
Rozenfel’d, B.A.: Non-Euclidean spaces, Moscow, 1969 (in Russian).
Rosenfeld, B.A. [B.A. Rozenfel’d]: A history of noneuclidean geometry, Springer, 1988 (translated from the Russian).
Berger, M.: Geometry, Springer, 1987 (translated from the French).
Coxeter, H.S.M.: Introduction to geometry, Wiley, 1963.
Greenberg, M.: Euclidean and non-euclidean geometry, Freeman, 1980.
Artmann, B.: Lineare Algebra, Birkhäuser, 1986.
Halmos, P.R.: Finite-dimensional vector spaces, v. Nostrand, 1958.
Coxeter, H.S.M.: ‘On complexes with transitive groups of automorphisms’, Ann. of Math. 35 (1934), 588–621.
Coxeter, H.S.M. and Moser, W.O.J.: Generators and relations for discrete groups, Springer, 1984.
Tits, J.: ‘Groupes simples et géométries associées’, in Proc. Internat. Congress of Mathematicians 1962, Dursholm, Mittag-Leffler Institute, 1963, pp. 197-221.
Bourbaki, N.: Groupes et algèbres de Lie, Eléments de mathématiques, Hermann, 1968, Chapts. 4-5.
Andreev, E.M.: ‘On convex polyhedra in Lobacevskiĭ spaces’, Math. USSR-Sb. 10, no. 3 (1970), 413–440. (Mat. Sb. 81 (1970), 445-478)
Andreev, E.M.: ‘On convex polyhedra of finite volume in Lobacevskiĭ space’, Math. USSR-Sb. 12, no. 2 (1970), 255–259. (Mat. Sb. 83 (1970), 256-260)
Makarov, V.S.: ‘On Fedorov groups of the four-and fivedimensional Lobachevskiĭ spaces’, in Studies in general algebra, Vol. 1, Kishinev, 1968, pp. 120-129 (in Russian).
Vinberg, E.B.: ‘Discrete groups generated by reflections in Lobacevskiĭ spaces’, Math. USSR-Sb. 1, no. 3 (1967), 429–444. (Mat. Sb. 72 (1967), 471-488)
Vinberg, E.B.: ‘On groups of unit elements of certain quadratic forms’, Math. USSR-Sb. 16, no. 1 (1972), 17–35. (Mat. Sb. 87(1972), 18-36)
Shephard, G.C. and Todd, J.A.: ‘Finite unitary reflection groups’, Canad. J. Math. 6 (1954), 274–304.
Zalesskiĭ, A.E. and Serezhkin, V.N.: ‘Finite linear groups generated by reflections’, Math. USSR-Izv. 17, no. 3 (1981), 477–503. (Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), 1279-1307)
Cohen, A.M.: ‘Finite quaternionic reflection groups’, J. of Algebra 64 (1980), 293–324.
Wagner, A.: ‘Determination of the finite primitive reflection groups over an arbitrary field of characteristic not 2, I’, Geom. Deö. 9 (1980), 239–253.
Wagner, A.: ‘Determination of the finite primitive reflection groups over an arbitrary field of characteristic not 2, II’, Geom. Deö. 10 (1981), 191–203.
Wagner, A.: ‘Determination of the finite primitive reflection groups over an arbitrary field of characteristic not 2, III’, Geom. Deö. 10 (1981), 475–523.
Courant, R. and Hilbert, D.: Methods of mathematical physics. Partial differential equations, 2, Interscience, 1965 (translated from the German).
Dunford, N. and Schwartz, J.T.: Linear operators. General theory, 1, Interscience, 1958.
Yosida, K.: Functionals analysis, Springer, 1980.
Kantorovich, L.V. and Akilov, G.P.: Functionals analysis, Pergamon, 1982 (translated from the Russian).
Beauzamy, B.: Introduction to Banach spaces and their geometry, North-Holland, 1982.
Day, M.M.: Normed linear spaces, Springer, 1973.
Dulst, D. van: Reflexive and superreflexive Banach spaces, MC Tracts, 102, Math. Centre, 1978.
Kleene, S.C.: Introduction to metamathematics, North-Holland & Noordhoff, 1959, p. 194ff.
Cramér, H.: Mathematical methods of statistics, Princeton Univ. Press, 1946.
Kendall, M.G. and Stuart, A.: The advanced theory of statistics, 2. Inference and relationship, Griffin, 1979.
Kendall, M.G. and Stuart, A.: The advanced theory of statistics, 2. Inference and relationship, Griffin, 1979.
Smirnov, N.V. and Dunin-Barkovskiĭ, N.V.: Mathematische Statistik in der Technik, Deutsch. Verlag Wissenschaft., 1969 (translated from the Russian).
Aĭvazyan, S.A.: Statistical research on dependence, Moscow, 1968 (in Russian).
Rao, C.R.: Linear statistical inference and its applications, Wiley, 1965.
Draper, N.R. and Smith, H.: Applied regression analysis, Wiley, 1981.
Härdle, W.: Applied nonparametric regression, Cambridge Univ. Press, 1990.
Kendall, M.G. and Stuart, A.: The advanced theory of statistics, 3. Design and analysis, and time series, Griffin, 1983.
Malinvaud, E.: Statistical methods of econometrics, North-Holland, 1970.
Theil, H.: Principles of econometrics, North-Holland, 1971.
Grenander, U. and Rosenblatt, M.: Statistical analysis of stationary time series, Wiley, 1957.
Gorenstein, D.: Finite groups, Chelsea, reprint, 1980.
Thompson, J.G.: ‘Finite groups with fixed-point-free automorphisms of prime order’, Proc. Nat. Acad. Sci. 45 (1959), 578–581.
Keldysh, M.V.: ‘On the solvability and stability of the Dirichlet problem’, Uspekhi Mat. Nauk 8 (1941), 171–232 (in Russian).
Landkof, N.S.: Foundations of modern potential theory, Springer, 1972 (translated from the Russian).
Hayman, W.K. and Kennedy, P.: Subharmonic functions, Acad. Press, 1976.
Bliedtner, J. and Hansen, W.: Potential theory. An analytic and probabilistic approach to balayage, Springer, 1986.
Lebesgue, H.: ‘Sur des cas d’impossibilité du problème de Dirichlet ordinaire’, C. R. Séances Soc. Math. France 41 (1913), 17.
Lebesgue, H.: ‘Conditions de régularité, conditions d’irrégularité, conditions d’impossibilité dans le problème de Dirichlet’, C. R. Acad. Sci. Paris 178 (1924), 349–354.
Wiener, N.: The Dirichlet problem’, J. Math. Phys. 3 (1924), 127–146.
Tsuji, M.: Potential theory in modem function theory, Chelsea, reprint, 1975.
Wermer, J.: Potential theory, Lecture notes in math., 408, Springer, 1981.
Clifford, A.H. and Preston, G.B.: The algebraic theory of semigroups, 1-2, Amer. Math. Soc, 1961-1967.
Lyapin, E.S.: Semigroups, Amer. Math. Soc, 1974 (translated from the Russian).
Kudryavtsev, V.B., Aleshin, S.V. and Podkolzin, A.S.: Elements of automata theory, Moscow, 1978 (in Russian).
Salomaa, A.: ‘Axiomatization of an algebra of events realizable by logical networks’, Probi Kibernet. 17 (1966), 237–246 (in Russian).
Yanov, Yu. L.: ‘Invariant operations over events’, Probi Kibernet 12 (1964), 253–258 (in Russian).
Yanov, Yu. L.: ‘Some subalgebras of events having no finite complete systems of identities’, Probl. Kibernet. 17 (1966), 255–258 (in Russian).
Ushchumlich, Sh.: ‘Investigation of some algorithms for the analysis and synthesis of automata’, Soviet Math. Dokl. 20 (1979), 771–775, (Dokl. Akad. Nauk SSSR 247, no. 3 (1979), 561-565)
Salomaa, A.: Theory of automata, Pergamon Press, 1969.
Conway, J.H.: Regular algebra and finite machines, Chapman & Hall, 1971.
Eilenberg, S.: Automata, languages and machines, A, Acad. Press, 1974.
Robin, M.O. and Scott, O.: ‘Finite automata and their decision problems’, IBM J. Res. Devel. 3 (1959), 114–125.
Bliss, G.A.: Lectures on the calculus of variations, Chicago Univ. Press, 1947.
Lavrent’ev, M.A. and Lyusternik, L.A.: A course in variational calculus, Moscow-Leningrad, 1950 (in Russian).
Cesari, L.: Optimization-theory and applications. Problems with ordinary differential equations, Springer, 1983.
Petrov, Yu. P.: Variational methods in optimum control theory, Acad. Press, 1968, Chapt. IV (translated from the Russian).
Springer, G.: Introduction to Riemann surfaces, Addison Wesley, 1957, p. 60; 169; 173.
Kantorovich, L.V., Vulikh, B.Z. and Pinsker, A.G.: Functionals analysis in semi-ordered spaces, Moscow-Leningrad, 1950 (in Russian).
Lyapunov, A.M.: Stability of motion, Acad. Press, 1966 (translated from the Russian).
Bylov, B.F., Vinograd, R.E., Grobman, D.M. and Nemytskiĭ, V.V.: The theory of the Lyapunov exponent and its application to questions of stability, Moscow, 1966 (in Russian).
Izobov, N.A.: ‘Linear systems of ordinary differential equations’, J. Soviet Math. 5, no. 1 (1976), 46–96. (Itogi Nauk. i Tekhn. Mat. Anal. 12, no. 1 (1974), 71-146)
Munroe, M.E.: Introduction to measure and integration, Addison Wesley, 1953, p. 111.
Hall, M.: The theory of groups, Macmillan, 1959.
Coxeter, H.S.M.: Regular complex polytopes, Cambridge Univ. Press, 1990, Chapt. 1.
Enzyklopädie der Elementarmathematik, 4. Geometrie, Deutsch. Verlag Wissenschaft, (translated from the Russian).
Lyusternik, L.A.: Convex figures and polyhedra, Moscow, 1956 (in Russian).
Shklyarskiĭ, D.O., Chentsov, N.N. and Yaglom, I.M.: The USSR Olympiad book: selected problems and theorems of elementary mathematics, Freeman, 1962 (translated from the Russian).
Coxeter, H.S.M.: Regular complex polytopes, Cambridge Univ. Press, 1990.
Grünbaum, B.: ‘Regular polyhedra-old and new’, Aequat. Math. 16 (1970), 1–20.
Senechal, M. and Flede, G. (eds.): Shaping space, Birkäuser, 1988.
Saffaro, L.: ‘Dai cinqui poliedri platonici all’infinito’, Encicl. Sci. e Tecn. Mondadori 76 (1976), 474–484.
Fejes Toth, L.: Regular figures, Pergamon, 1964 (translated from the German).
Shanks, D.: Solved and unsolved problems in number theory, Chelsea, reprint, 1978.
Curtis, C.W. and Reiner, I.: Methods of representation theory, 1-2, Wiley (Interscience), 1981-1987.
Zariski, O. and Samuel, P.: Commutative algebra, 2, Springer, 1975.
Serre, J.-P.: Algèbre locale. Multiplicités, Springer, 1965.
Grothendieck, A. and Dieudonné, J.: ‘Eléments de géométrie algébrique. I. Le langage des schémas’, Publ. Math. IHES 4 (1964).
Bourbaki, N.: Algèbre commutative, Masson, 1983.
Dauns, J. and Hofmann, K.: ‘The representation of biregular rings by sheaves’, Math. Z 91 (1966), 103–123.
Lambek, J.: Lectures on rings and modules, Blaisdell, 1966.
Skornyakov, L.A.: Complemented modular lattices and regular rings, Oliver & Boyd, 1962 (translated from the Russian).
Faith, C.: Algebra, 1-2, Springer, 1973-1976.
Tsukerman, G.M.: ‘Ring of endomorphisms of a free module’, Sib. Math. J. 7, no. 5 (1966), 923–927. (Sibirsk. Mat. Zh. 7, no. 5 (1966), 1161-1167)
Shaĭn, B.M.: ‘O-rings and LA-rings’, Izv. Vyssh. Uchebn. Mat, no. 2 (1966), 111-122 (in Russian).
Goodearl, K.R.: Von Neumann regular rings, Pitman, 1979.
Kaplansky, I.: Rings of operators, Benjamin, 1968.
Neumann, J. von: Continuous geometries, Princeton Univ. Press, 1960.
Whitney, H.: ‘On the abstract properties of linear dependence’, Amer. J. Math. 57 (1935), 509–533. (Reprinted in: Joseph P.S. Kung (ed.), A source book in matroid theory, Birkhäuser, 1986, pp. 55-80).
Aigner, M.: Combinatorial theory, Springer, 1979, Chapt. II (translated from the German).
Koppelberg, S.: ‘General theory of Boolean algebras’, in J.D. Monk and R. Bonnet (eds.): Handbook of Boolean Algebras, Vol. 1, North-Holland, 1989, p. 283.
Myers, D. de: ‘Lindenbaum-Tarski algebras’, in J.D. Monk and R. Bonnet (eds.): Handbook of Boolean Algebras, Vol. 3, North-Holland, 1989, pp. 1167-1195.
Abhyankar, S.S.: ‘On the problem of resolution of singularities’, in LG. Petrovskii (ed.): Proc. Internat. Congress of Mathematicians Moscow, 1966, Moscow, 1968, pp. 469-481.
Mumford, D.: Lectures on curves on an algebraic surface, Princeton Univ. Press, 1966.
Hironaka, H.: ‘Resolution of singularities of an algebraic variety over a field of characteristic zero I, 11’, Ann. of Math. 79 (1964), 109–203; 205-326.
Hartshorne, R.: Algebraic geometry, Springer, 1977.
Clifford, A. and Preston, G.: Algebraic theory of semigroups, 1-2, Amer. Math. Soc, 1961-1967.
Munn, W.D.: ‘Regular co-semigroups’, Glasgow Math. J. 9, no. 1 (1968), 46–66.
Clifford, A.: ‘The fundamental representation of a regular semigroup’, Semigroup Forum 10 (1975), 84–92.
Clifford, A.: ‘A structure theorem for orthogroups’, J. Pure Appl. Algebra 8 (1976), 23–50.
Nambooripad, K.S.S.:’ structure of regular semigroups, I’, Mem. Amer. Math. Soc. 22, no. 224 (1979).
Nambooripad, K.S.S.: ‘The natural partial order on a regular semigroup’, Proc. Edinburgh Math. Soc. 23, no. 3 (1980), 249–260.
Nambooripad, K.S.S. and Rajan, A.R.: ‘Structure of combinatorial regular semigroups’, Quart. J. Math. 29, no. 116 (1978), 489–504.
Grillet, P.A.: ‘The structure of regular semigroups, I-IV, Semigroup Forum 8 (1974), 177–183; 254-265; 368-373.
Hall, T.E.: ‘Orthodox semigroups’, Pacific. J. Math. 39 (1971), 677–686.
Hall, T.E.: ‘On regular semigroups’, J. of Algebra 24 (1973), 1–24.
Meakin, J. and Nambooripad, K.S.S.: ‘Coextensions of pseudo-inverse semigroups by rectangular bands’, J. Austral. Math. Soc. 30 (1980/81), 73–86.
Warne, R.J.: ‘Natural regular semigroups’, in G. Pollàk (ed.): Algebraic Theory of Semigroups, North-Holland, 1979, pp. 685-720.
Lallement, G.: ‘Structure theorems for regular semigroups’, Semigroup Forum 4 (1972), 95–123.
Dunford, N. and Schwartz, J.: Linear operators, 1. General theory, Wiley, 1988.
Aleksandrov, A.D.: ‘Additive set-functions in abstract spaces’, Mat. Sb. 9 (1941), 563–628 (in Russian).
Golubev, V.V.: Vorlesungen über Differentialgleichungen im Komplexen, Deutsch. Verlag Wissenschaft., 1958 (translated from the Russian).
Coddington, E.A. and Levinson, N.: Theory of ordinary differential equations, McGraw-Hill, 1955.
Levelt, A.H.M.: ‘Hypergeometric functions I-IV, Proc. Koninkl. Nederl. Akad. Wet. Ser. A 64, no. 4 (1961), 362–403.
Deligne, P.: Equations différentielles à points singuliers réguliers, Lecture notes in math., 163, Springer, 1970.
Plemelj, J.: Problems in the sense of Riemann and Klein, Wiley, 1964.
Arnol’d, V.I. and Il’yashenko, Yu. S.: Ordinary differential equations, Encycl. math, sci., 1, Springer, Forthcoming (translated from the Russian).
Bateman, H. and Erdélyi, A.: Higher transcendental functions, 3. Automorphic functions, McGraw-Hill, 1955.
Kelley, J.L.: General topology, Springer, 1975.
Arkhangel’skiĭ, A.V. and Ponomarev, V.I.: Fundamentals of general topology: problems and exercises, Reidel, 1984 (translated from the Russian).
Cech, E.: Topological spaces, Wiley, 1966, p. 492ff.
Hardy, G.H.: Divergent series, Clarendon, 1949.
Cooke, R.G.: Infinite matrices and sequence spaces, Macmillan, 1950.
Kangro, G.F.: ‘Theory of summability of sequences and series’, J. Soviet Math. 5, no. 1 (1976), 1–45. (Itogi Nauk. i Tekhn. Mat. Anal. 12 (1974), 5-70)
Baron, S.: Introduction to theory of summation of series, Talin, 1977 (in Russian).
Borel, A.: Linear algebraic groups, Benjamin, 1969.
Humphreys, J.E.: Linear algebraic groups, Springer, 1975.
Toeplitz, O.: Prace Mat. Fiz. 22 (1911), 113–119.
Steinhaus, H.:’ some remarks on the generalization of the concept of limit’, in Sel. Math. Papers, Polish Acad. Sci., 1985, pp. 88-100.
Hardy, G.H.: Divergent series, Clarendon, 1949.
Cooke, R.G.: Infinite matrices and sequence spaces, Macmillan, 1950.
Hawking, S.W.: ‘Zeta function regularization of path integrals’, Comm. Math. Phys. 55 (1977), 133–148.
Gamboa Saravi, R.E., Muschietti, M.A. and Solomin, J.E.: ‘On the quotient of the regularized determinant of two elliptic operators’, Comm. Math. Phys. 110 (1987), 641–654.
Kress, R.: Linear integral equations, Springer, 1989, Chapt. 5.
Treves, F.: Pseudodifferential and Fourier integral operators, 1-2, Plenum, 1980.
Tikhonov, A.N. and Arsenin, V. Ya.: Solutions of ill-posed problems, Wiley, 1977 (translated from the Russian).
Tikhonov, A.N.: ‘Solution of incorrectly formulated problems and the regularization method’, Soviet Math. Dokl 4, no. 4 (1963), 1035–1038. (Dokl. Akad. Nauk SSSR 151, no. 3 (1963), 501-504)
Tikhonov, A.N.: ‘Regularization of incorrectly posed problems’, Soviet Math. Dokl. 4, no. 6 (1963), 1624–1627. (Dokl. Akad. Nauk SSSR 153, no. 1 (1963), 49-52)
Lavrentiev, M.M. [M.M. Lavrent’ev]: Some improperly posed problems of mathematical physics, Springer, 1967 (translated from the Russian).
Bertero, M. and Viano, G.: ‘On probabilistic methods for the solution of improperly posed problems’, Boll. Un. Mat. Ital. 15-B (1978), 483–508.
Engl, H.W. and Groetsch, C.W. (eds.): Inverse and illposed problems, Acad. Près, 1987.
Hilgers, J.: ‘On the equivalence of regularization and certain reproducing kernel Hilbert space approaches for solving first kind problems’, SIAM J. Numer. Anal. 13 (1976), 172–184.
Hoerl, A. and Kennard, R.: ‘Ridge regression’, Technometrics 12 (1970), 55–82.
Hofmann, B.: Regularization for applied inverse and ill-posed problems, Teubner, 1986.
Louis, A.: Inverse und schlecht gestellte Probleme, Teubner, 1989.
Nashed, M.Z. and Wahba, G.: ‘Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind’, Math. Comp. 28 (1974), 69–80.
Varah, J.: ‘A practical examination of some numerical methods for linear discrete ill-posed problems’, SIAM Rev. 21 (1979), 100–111.
Mandelbrojt, S.: Séries adhérentes, régularisations des suites, applications, Gauthier-Villars, 1952.
Siddigi, J.A.: ‘On the equivalence of classes of infinitely differentiable functions’, Soviet J. Contemp. Math. Anal. Arm. Acad. Sci. 19, no. 1 (1984), 18–29. (Izv. Akad. Nauk Arm. SSR. Mat. 19, no. 1 (1984), 19-30)
Koblitz, N.: p-adic numbers, p-adic analysis, and zetafunctions, Springer, 1977, Chapt. IV, §3-4.
Borevich, Z.I. and Shafarevich, I.R.: Number theory, Acad. Press, 1987 (translated from the Russian).
Lang, S.: Algebraic number theory, Addison-Wesley, 1970.
Reidemeister, K.: ‘Homotopieringe und Linsenräume’, Abh, Math. Sem. Univ. Hamburg 11 (1935), 102–109.
Franz, W.: ‘Ueber die Torsion einer Ueberdeckung’, J. Reine Angew. Math. 173 (1935), 245–254.
Rham, G. de: ‘Sur les nouveaux invariants de M. Reidemeister’, Mat. Sb. 1, no. 5 (1936), 737–743.
Bass, H.: ‘K-theory and stable algebra’, Publ. Math. IHES 22 (1964), 5–60.
Milnor, J.: ‘Whitehead torsion’, Bull. Amer. Math. Soc. 72 (1966), 358–426.
Vladimirov, V.S.: Methods of the theory of functions of many complex variables, M.I.T., 1966 (translated from the Russian).
Shabat, B.V.: Introduction to complex analysis, Moscow, 1985 (in Russian).
Hörmander, L.: An introduction to complex analysis in several variables, North-Holland, 1973.
Range, R.M.: Holomorphic functions and integral represen tations in several complex variables, Springer, 1986.
Bell, J. and Machover, M.: A course in mathematical logic, North-Holland, 1977.
Müller, E.: Monatsh. Math, und Physik 31 (1921), 3–19.
Norden, A.P.: ‘Sur l’inclusion des théories métriques et affines des surfaces dans la géométrie des systèmes spécifiques’, C.R. Acad. Sci. Paris 192 (1931), 135–137.
Norden, A.P.: ‘On the intrinsic geometry of second kind hypersurfaces in affine space’, Izv. Vyzov. Mat. 4 (1958), 172–183 (in Russian).
Norden, A.P.: Spaces with an affine connection, Moscow, 1976 (in Russian).
MacLane, S.: Homology, Springer, 1963.
Moore, J.C. and Eilenberg, S.: Foundations of relative homological algebra, Amer. Math. Soc, 1965.
Sklyarenko, E.G.: Homology and cohomology of general spaces, Springer, Forthcoming (translated from the Russian).
Spanier, E.H.: Algebraic topology, McGraw-Hill, 1966.
Switzer, R.M.: Algebraic topology-homotopy and homology, Springer, 1975.
Tits, J.: ‘Sur la classification des groupes algébriques semisimples’, C.R. Acad. Sci. Paris 249 (1959), 1438–1440.
Borel, A. and Tits, J.: ‘Groupes réductifs’, Publ. Math. IH ES 27 (1965), 55–150.
Tits, J.: ‘Classification of algebraic simple groups’, in Algebraic Groups and Discontinuous Subgroups, Proc. Symp. Pure Math., Vol. 9, Amer. Math. Soc, 1966, pp. 33-62.
Kelley, J.L.: General topology, v. Nostrand, 1955, p. 50ff.
Alexandroff, P. [P.S. Aleksandrov] and Hopf, H.: Topologie, Chelsea, reprint, 1972, p. 33ff, 44ff.
Kuratowski, K.: Introduction to set theory and topology, Pergamon, 1961, p. 128ff (translated from the French).
Zel’dovich, Ya. B. and Novikov, I.D.: Relativistic astrophysics, Moscow, 1967 (in Russian).
Zel’dovich, Ya. B. and Novikov, I.D.: Relativistic astrophysics I. Stars and relativity, Chicago, 1971 (translated from the Russian).
Zel’dovich, Ya. B. and Novikov, I.D.: Relativistic astrophysics II. Structure and evolution of the Universe, Chicago, 1983 (translated from the Russian).
Peebles, P.J.E.: Physical cosmology, Princeton Univ. Press, 1971.
Misner, C.W., Thorne, K.S. and Wheeler, J.A.: Gravitation, Freeman, 1973, Chapt. 30.
Lifshits, E.M.: ‘On the gravitational stability of the expanding universe’, Zh. Eksper. i Teor. Fiz. 16 (1946), 587–602 (in Russian). English abstract.
Belinskiĭ, V.A., Lifshits, E.M. and Khalatnikov, I.M.: Uspekhi Fiz. Nauk 102 (1970), 463–500.
Braginskiĭ, V.A.: Uspekhi Fiz. Nauk 86 (1965), 433–446.
Zeldovich, Ya. B., Ruzmaĭkin, A.A. and Sokoloff, D.D. [D.D. Sokolov]: Magnetic fields in astrophysics, Gordon & Breach, 1983 (translated from the Russian).
Rees, M.J.: Phys. Rev. Letters 28 (1972), 1669–1671.
Penrose, R.:’ singularities and time-asymmetry’, in S. Hawking and W. Israel (eds.): General Relativity, an Einstein Centenary Survey, Cambridge Univ. Press, 1979, pp. 581-638.
Landsberg, P.T. and Evans, D.E.: Mathematical cosmology, Clarendon Press, 1977.
Hawking, S.W. and Ellis, G.F.R.: The large scale structure of space-time, Cambridge Univ. Press, 1973.
Weinberg, S.: Gravitation and cosmology, Wiley, 1972.
Chandrasekhar, S.: The mathematical theory of black holes, Oxford Univ. Press, 1983.
Ehlers, J. (ed.): Relativity theory and astrophysics, 1-3, Amer. Math. Soc., 1967.
Novikov, I.D. and Frolov, V.P.: Physics of black holes, Kluwer, 1989 (translated from the Russian).
Landau, L.D. and Lifshitz, E.M.: The theory of fields, Pergamon, 1965 (translated from the Russian).
Rindler, W.: Essential relativity, Springer, 1977.
Landau, L.D. and Lifshitz, E.M.: Fluid mechanics, Pergamon, 1959 (translated from the Russian).
Zel’dovich, Ya. B. and Novikov, I.D.: Relativistic astrophysics, 1. Stars and relativity, Chicago, 1971 (translated from the Russian).
Zel’dovich, Ya. B. and Novikov, I.D.: Relativistic astrophysics, 2. Structure and evolution of the Universe, Chicago, 1983 (translated from the Russian).
Misner, C.W., Thorne, K.S. and Wheeler, J.A.: Gravitation, Freeman, 1973, Chapt. 22.
Lichnerowicz, A.: Relativistic hydrodynamics and magne-tohydrodynamics, Benjamin, 1967.
Anile, A. and Choquet-Bruhat, Y. (eds.): Relativistic fluid dynamics, Lecture notes in math., 1385, Springer, 1989.
Fok, V.A.: Einstein’s theory and physical relativity, Moscow, 1967 (in Russian).
Rindler, W.: Essential relativity, Springer, 1977.
Landau, L.D. and Lifshitz, E.M.: Statistical physics, Pergamon, 1980 (translated from the Russian).
Misner, C.W., Thorne, K.S. and Wheeler, J.A.: Gravitation, Freeman, 1973.
Møller, C.: The theory of relativity, Clarendon Press, 1952.
Yuen, C.K.: Amer. J. Phys. 38 (1970), 246.
Anile, A. and Choquet-Bruhat, Y. (eds.): Relativistic fluid dynamics, Springer, 1989.
Kluitenberg, G.A. and Groot, S.R. de: ‘Relativistic thermodynamics of irreversible processes III’, Physica 20 (1954), 199–209.
Tolman, R.C.: Relativity, thermodynamics and cosmology, Clarendon Press, 1934.
Rindler, W.: Essential relativity, Springer, 1977, Chapt. 1.
Sachs, R.K. and Wu, H.: General relativity for mathematicians, Springer, 1977.
Eddington, A.S.: The mathematical theory of relativity, Cambridge Univ. Press, 1960.
Trench, A.P.: Special relativity, Norton & Cy, 1968.
Bergmann, P.G.: Introduction to the theory of relativity, Dover, reprint, 1976.
Einstein, A.: ‘Elektrodynamik bewegter Körper’, Ann. der Phys. 17 (1905), 891–921.
Einstein, A. and Infeld, L.: The evolution of physics, Simon & Schuster, 1962.
Minkowski, H.: ‘Raum und Zeit’, Phys. Z 10 (1909), 104–111.
Landau, L.D. and Livschits, E.M.: The classical theory of fields, Pergamon, 1975 (translated from the Russian).
Feynman, R., Leighton, R. and Sands, M.: The Feynman lectures on physics, 2, Addison-Wesley, 1965.
Pauli, W.: Relativitätstheorie, Teubner, 1921.
Synge, J.L.: Relativity: the general theory, North-Holland, 1960.
Tolman, R.: Relativity, thermodynamics and cosmology, Clarendon Press, 1969.
Rashewski, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
Fock, V.A. [V.A. Fok]: The theory of space, time and gravitation, Macmillan, 1954 (translated from the Russian).
Weyl, H.: Raum, Zeit, Materie, Springer, 1923.
Penrose, R.: ‘The structure of space-time’, in CM. DeWitt and J.A. Wheeler (eds.): Batelle Rencontre in Math, and Physics, Benjamin, 1968, pp. 121-235.
Schouten, J.A.: Tensor analysis for physicists, Cambridge Univ. Press, 1951.
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Synge, J.L. and Schild, A.: Tensor calculus, Toronto Univ. Press, 1959.
Sachs, R.K. and Wu, H.: General relativity for mathematicians, Springer, 1977. [A8] Lawden, D.F.: An introduction to tensor calculus and relativity, Methuen, 1962.
Eddington, A.S.: The mathematical theory of relativity, Cambridge Univ. Press, 1960.
Einstein, A., et al.: The principle of relativity. A collection of original papers, Dover, reprint, 1952.
Einstein, A.: The meaning of relativity, Princeton Univ. Press, 1956.
Young, D.M.: ‘Iterative methods for solving partial differential equations of elliptic type’, Trans. Amer. Math. Soc. 76, no. 1 (1954), 92–111.
Young, D.M.: Iterative solution of large linear systems, Acad. Press, 1971.
Wasow, W. and Forsyth, J.: Finite-difference methods for partial differential equations, Wiley, 1960.
Faddeev, D.K. and Faddeeva, V.N.: Computational methods of linear algebra, Freeman, 1963 (translated from the Russian).
Hageman, L.A. and Young, D.M.: Applied iterative methods, Acad. Press, 1981.
Andronov, A.A., Vitt, A.A. and Khaĭkin, S.E.: Theory of oscillators, Dover, reprint, 1987 (translated from the Russian).
Landa, N.S.: Auto-oscillations in systems with a finite number of degrees of freedom, Moscow, 1980 (in Russian).
Romanovskiĭ, Yu. M., Stepanova, N.V. and Chernavskiĭ, D.S.: Mathematical modelling in biophysics, Moscow, 1975 (in Russian).
Pol, B. van der: Phil. Mag Ser. 7 2, no. 11 (1926), 978–992.
Zheleztsov, N.A. and Rodygin, L.V.: Dokl Akad. Nauk SSSR 81, no. 3(1951), 391–394.
Anosov, D.V.: ‘Limit cycles of systems of differential equations with small parameters in front of the highest derivatives’, Mat. Sb. 50, no. 3 (1960), 299–334 (in Russian).
Doronitsyn, A.A.: ‘Asymptotic solution of van der Pol’s equation’, Prikl. Mat. i Mekh. 11, no. 3 (1947), 313–328 (in Russian). English abstract.
Zharov, M.I., Mishchenko, E.F. and Rozov, N. Kh.: ‘On some special functions and constants arising in the theory of relaxation oscillations’, Soviet Math. Dokl. 24, no. 3 (1981), 672–675. (Dokl. Akad. Nauk SSSR 261, no. 6 (1981), 1292-1296)
Mishchenko, E.F. and Rozov, N. Kh.: Differential equations with small parameters and relaxation oscillations, Plenum, 1980 (translated from the Russian).
Rozov, N. Kh.: ‘Asymptotic computation of solutions of systems of second-order differential equations close to discontinuous periodic solutions’, Soviet Math. Dokl. 3, no. 4 (1962), 932–934. (Dokl. Akad. Nauk SSSR 145, no. 1 (1962), 38-40)
Pontryagin, L.S.: ‘Asymptotic behaviour of solutions of systems of differential equations with a small parameter in front of the highest order derivatives’, Izv. Akad. Nauk SSSR Ser. Mat. 21, no. 5 (1957), 605–626 (in Russian).
Mishchenko, E.F.: ‘Asymptotic calculation of periodic solutions of differential equations with small parameters in front of the derivatives’, Izv. Akad. Nauk SSSR Ser. Mat. 21, no. 5 (1957), 627–654 (in Russian).
Levi, M.: Qualitative analysis of the periodically forced relaxation oscillations, Amer. Math. Soc, 1981.
Grasman, J.: Asymptotic methods for relaxation oscillations and applications, Springer, 1987.
Callot, J.L., Diener, F. and Diener, M.: ‘Le problème de la “chasse au canard”’, C.R. Acad. Sci. Paris A286 (1987), 1059–1061.
Chang, K.W. and Howes, F.A.: Nonlinear singular perturbation phenomena: theory and application, Springer, 1984.
Eckhaus. W.: Asymptotic analysis of singular perturbations, North-Holland, 1979.
O’Malley, R.E., Jr.: Introduction to singular perturbations, Acad. Press, 1974.
Levinson, N.: ‘Perturbations of discontinuous solutions of nonlinear systems of differential equations’, Acta Math. 82 (1950), 71–106.
Lebovitz, N.R. and Schaar, R.: ‘Exchange of stabilities in autonomous systems’, Studies Appl. Math. 54 (1975), 229–260.
Levin, J. and Levinson, N.: ‘Singular perturbations of nonlinear systems of differential equations and an associated boundary layer equation’, J. Rat. Mech. Anal. 3 (1954), 247–270.
Takens, F.: ‘Constrained equations: a study of implicit differential equations and their discontinuous solutions’, in P. Hilton (ed.): Structural Stability, the Theory of Catastrophes, and Applications in the Sciences, Springer, 1976, pp. 143-234.
Sastry, S.S., Desoer, C.A. and Varaiya, P.P.: ‘Jump behaviour of circuits and systems’, IEEE Trans. Circuits and Systems (1980).
Nayfeh, A.: Perturbation methods, Wiley, 1973.
Rabinovich, M.I. and Trubetskov, D.I.: Oscillations and waves in linear and nonlinear systems, Kluwer, 1989 (translated from the Russian).
Shannon, C.: ‘A symbolic analysis of relay and switching circuits’, AIEE Trans. 57 (1938), 713–723.
Gavrilov, M.A.: Relaisschalttechnik, Deutsch. Verlag Wissenschaft., 1953 (translated from the Russian).
Shestakov, V.I.: ‘On a logical calculus applicable to the theory of relay-contact circuits’, Uchen. Zap. Moskov. Gosudarstv. Univ. Mat. 73, no. 5 (1944), 45–48 (in Russian).
Lupanov, O.B.: ‘Complexity of relay-contact circuits realization by functions of the algebra of logic’, Probl. Kibernetiki 11 (1964), 25–47 (in Russian).
Chegis, I.A. and Yablonskii, S.V.: ‘Logical means for controlling the functioning of electric systems’, Trudy Mat. Inst. Steklov. 51 (1958), 270–360 (in Russian).
Solov’ev, N.A.: Tests, Novosibirsk, 1978 (in Russian).
Potapov, Yu. G. and Yablonskii, S.V.: ‘On the synthesis of self-correcting relay circuits’, Soviet Phys. Dokl. 5 (1961), 932–935. (Dokl. Akad. Nauk SSSR 134, no. 3 (1960), 544-547)
Neumann, J. von: ‘Probabilistic logics and the synthesis of reliable organisms from unreliable components’, in Automata Studies, Princeton Univ. Press, 1956, pp. 43-98.
Moore, E.F. and Shannon, C.E.: ‘Reliable circuits using less reliable relays I, II’, J. Franklin Inst. 262 (1956), 198–208; 281-297
Barzilovich, E. Yu. and Kashtanov, V.A.: Some mathematical problems in the theory of maintenance of complex systems, Moscow, 1971 (in Russian).
Barlow, R.E. and Proschan, F.: Mathematical theory of reliability, Wiley, 1965.
Barlow, R.E. and Proschan, F.: Statistical theory of reliability and lifetesting:, Holt, Rinehart & Winston, 1975.
Gnedenko, B.V., Belyaev, Yu. K. and Solov’ev, A.D.: Mathematical methods of reliability theory, Acad. Press, 1969 (translated from the Russian).
Kovalenko, I.N.: Studies in the analysis of reliability of complex systems, Kiev, 1975 (in Russian).
Kozlov, B.A. and Ushakov, I.A.: Reliability handbook, Holt, Rinehart & Winston, 1970 (translated from the Russian).
Shor, Ya. B.: Statistical methods in analysis and control of quality and reliability, Moscow, 1962 (in Russian).
Gertsbakh, I.B.: Statistical reliability theory, Birkhäuser, 1989 (translated from the Russian).
Pieruschka, E.: Principles of reliability, Prentice-Hall, 1963.
Pierce, W.H.: Failure tolerant computer design, Acad. Press, 1965.
Beichelt, F. and Franken, P.: Zuverlässigkeit und Instandhaltung, VEB Verlag Technik, 1983.
Bleistein, N. and Handelsman, R.A.: Asymptotic expansions of integrals, Dover, reprint, 1986,Chapts. 1, 3, 5.
Davis, P.J.: Interpolation and approximation, Dover, reprint, 1975.
Spivak, M.: Calculus, Benjamin, 1967.
Inasaridze, H.N.: ‘A generalization of perfect mappings’, Soviet Math. Dokl. 7, no. 3 (1966), 620–622. (Dokl. Akad. Nauk SSSR 168 (1966), 266-268)
Vinogradov, I.M.: Elements of number theory, Dover, reprint, 1954 (translated from the Russian).
Hardy, G.H. and Wright, E.M.: An introduction to the theory of numbers, Oxford Univ. Press, 1979.
Zoretti, L.: Leçons sur le prolongement analytique, Gauthier-Villars, 1911.
Ahlfors, L.V.: ‘Bounded analytic functions’, Duke Math. J. 14, no. 1 (1947), 1–11.
Nohiro, K.: Cluster sets, Springer, 1960.
Khavinson, S. Ya.: ‘Analytic functions of bounded type’, Itogi Nauk. Mat. Anal. 1963 (1965), 5–80 (in Russian).
Carleson, L.: Selected problems on exceptional sets, v. Nostrand, 1967.
Mel’nikov, M.S. and Sinanyan, S.O.: ‘Aspects of approximation theory for functions of one complex variable’, J. Soviet Math. 5, no. 5 (1976), 688–752. (Itogi Nauk. i Tekhn. Sovremen. Probl. Mat. 4 (1975), 143-250)
Shabat, B.V.: Introduction to complex analysis, 2, Moscow, 1985 (in Russian).
Hayman, W.K. and Kennedy, P.B.: Subharmonic functions, 1, Acad. Press, 1976.
Dolzhenko, E.P.: ‘Elimination of singularities of analytic functions’, Uspekhi Mat. Nauk 18, no. 4 (1963), 135–142 (in Russian).
Riihentaus, L.J.: ‘Removable singularities of analytic functions of several complex variables’, Math. Z. 158 (1978), 45–54.
Gunning, R.C. and Rossi, H.: Analytic functions of several complex variables, Prentice-Hall, 1965.
Harvey, R. and Polking, J.: ‘Removable singularities of solutions of linear partial differential equations’, Acta Math. 125 (1970), 39–55.
Garnett, J.B.: Analytic capacity and measure, Springer, 1972.
Chirka, E.M.: Complex analytic sets, Kluwer, 1989 (translated from the Russian).
Markushevich, A.I.: Theory of functions of a complex variable, 1, Chelsea, 1977 (translated from the Russian).
Cox, D.R.: Renewal theory, Methuen, 1962.
Bethe, H.A.: The electromagnetic shift of energy levels’, Phys. Rev. 72 (1947), 339–341.
Bogolyubov, N.N. and Parasyuk, O.S.: ‘On the theory of multiplication of causal singular functions’, Dokl. Akad. Nauk SSSR 100, no. 1 (1955), 25–28 (in Russian).
Bogolyubov, N.N. and Parasyuk, O.S.: ‘On the subtractive formalism in multiplication of causal singular functions’, Dokl. Akad. Nauk SSSR 100, no. 3 (1955), 429–432 (in Russian).
Zavialov, O.I. [O.I. Zav’yalov]: Renormalized quantum field theory, Kluwer, 1990 (translated from the Russian).
Hepp, K.: Théorie de la renormalisation, Lecture notes in physics, 2, Springer, 1969.
Manoukian, E.B.: Renormalization, Acad. Press, 1983.
Rényi, A.: ‘On the theory of order statistics’, Acta Math. Acad. Sci. Hungar. 4 (1953), 191–231.
Häzjek, J. and Sidák, Z.: Theory of rank tests, Acad. Press, 1967.
Bol’shev, L.N. and Smirnov, N.V.: Tables of mathematical statistics, Libr. of mathematical tables, 46, Nauka, Moscow, 1983 (in Russian). Processed by L.S. Bark and E.S. Kedrova.
Il’in, V.A. and Poznyak, E.G.: Fundamentals of mathematical analysis, 1-2, Mir, 1982 (translated from the Russian).
Kolmogorov, A.N. and Fomin, S.V.: Elements of the theory of functions and functional analysis, 1-2, Graylock, 1957-1961 (translated from the Russian).
Kudryavtsev, L.D.: A course in mathematical analysis, 2, Moscow, 1981 (in Russian).
Nikol’skiĭ, S.M.: A course of mathematical analysis, 2, Mir, 1977 (translated from the Russian).
Smirnov, V.I.: A course of higher mathematics, 5, Addison-Wesley, 1964 (translated from the Russian).
Hewitt, E. and Stromberg, K.: Real and abstract analysis, Springer, 1965.
Rudin, W.: Real and complex analysis, McGraw-Hill, 1978.
Saks, S.: Theory of the integral, Hafner, 1952 (translated from the Polish).
Apostol, T.M.: Mathematical analysis, Addison-Wesley, 1974.
Halmos, P.R.: Measure theory, Springer, 1974.
Zaanen, A.C.: Integration, North-Holland, 1974.
Knopp, K.: Theorie und Anwendung der unendlichen Reihen, Springer, 1964. (Incomplete English translation: Blackie, 1928).
Bahtia, N.P. and Szegö, G.P.: Stability theory of dynamical systems, Springer, 1970.
Guckenheimer, J. and Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, 1983.
Ruelle, D.: ‘Small random perturbations of dynamical systems and the definition of attractors’, Comm. Math. Phys. 82 (1981), 137–151.
Mal’tsev, A.I.: Algebraic systems, Springer, 1973 (translated from the Russian).
Chevalley, C.: Théorie des groupes de Lie, II: Groupes algébriques, Hermann, 1951, Chapt. II, §14.
Serre, J.P.: Lie algebras and Lie groups, Benjamin, 1965.
Théorie des algébres de Lie. Topologie des groupes de Lie, Sem. S. Lie 1954/55, Secr. Math. Univ. Paris, 1955.
Chevalley, C.: Théorie des groupes de Lie, 2, Hermann, 1951.
Bourbaki, N.: Groupes et algébres de Lie, Hermann, 1975, Chapts. 7-8.
Artin, M.: Algebraic spaces, Yale Univ. Press, 1971.
Grothendieck, A. and Dieudonné, J.: Éléments de géométrie algébrique, I. Le langage des schémes, Springer, 1971.
MacLane, S.: Categories for the working mathematician, Springer, 1971.
Grothendieck, A. and Dieudonné, J.: ‘Eléments de géométrie algébriques III’, Publ. Math. IHES 11 (1961), 349–356.
Grothendieck, A.: ‘Fondements de la géométrie algébrique’, Sém. Bourbaki 195; 221; 232 (1960-1962).
Artin, M.: ‘Algebraization of formal moduli, I’, in D.C. Spencer and S. lyanaga (eds.): Global Analysis (papers in honor of K. Kodaira), Princeton Univ. Press, 1969, pp. 21-72.
Cartan, E.: ‘Sur la détermination d’un système orthogonal complet dans un espace de Riemann symmétrique clos’, Rend. Circ. Mat. Palermo 53 (1929), 217–252.
Van Cha Dao: ‘Spherical sections on a compact homogene ous space’, Uspekhi Mat. Nauk 30, no. 5 (1975), 203–204 (in Russian).
Dzyadyk, Yu. V.: ‘On the determination of the spectrum of an induced representation on a compact symmetric space’, Soviet Math. Dokl. 16 (1975), 193–197. (Dokl. Akad. Nauk SSSR 220, no. 5 (1975), 1019-1022)
Lukatskiĭ, A.M.: Uspekhi Mat. Nauk 26, no. 5 (1971), 212–213.
Onishchik, A.L.: ‘On invariants and almost invariants of compact transformation groups’, Trans. Moscow Math. Soc. 35 (1976), 237–267. (Trudy Moskov. Mat. Obshch. 35 (1976), 235-264)
Helgason, S.: Groups and geometric analysis, Acad. Press, 1984.
Pontryagin, L.S.: Topological groups, Princeton Univ. Press, 1958 (translated from the Russian).
Naĭmark, M.A.: Theory of group representations, Springer, 1982 (translated from the Russian).
Zhelobenko, D.P.: Compact Lie groups and their representations, Amer. Math. Soc, 1973 (translated from the Russian).
Lang, S.: SL2(R), Addison-Wesley, 1975.
Gel’fand, I.M., Graev, M.I. and Pyatetskiĭ-Shapiro, I. I.: Generalized functions, 6. Representation theory and automorphic functions, Saunders, 1969 (translated from the Russian).
Serre, J.-P.: Abelian l-adic representations and elliptic curves, Benjamin (translated from the French).
Chevalley, C.: Theory of Lie groups, 1, Princeton Univ. Press, 1946.
Bourbaki, N.: Groupes et algèbres de Lie, Eléments de mathématique, Masson, 1982, Chapt. 9. Groupes de Lie réels compacts.
Bröcker, Th. and Tom Dieck, T.: Representations of compact Lie groups, Springer, 1985.
Hewitt, E. and Ross, K.A.: Abstract harmonic analysis, II, Springer, 1970.
Wawrzynczyk, A.: Group representations and special functions, Reidel & PWN, 1984.
Zhelobenko, D.P.: Compact Lie groups and their representations, Amer. Math. Soc, 1973 (translated from the Russian).
Kirillov, A.A.: Elements of the theory of representations, Springer, 1976 (translated from the Russian).
Naĭmark, M.A.: Theory of group representations, Springer, 1982 (translated from the Russian).
Zhelobenko, D.P. and Shtern, A.I.: Representations of Lie groups, Moscow, 1981 (in Russian).
Benson, D.: Modular representation theory: New trends and methods, Lecture notes in math., 1081, Springer, 1984.
Curtis, C.W. and Reiner, I.: Methods of representation theory, I-II, Wiley (Interscience), 1981-1987.
Feit, W.: The representation theory of finite groups, North-Holland, 1982.
Serre, J.-P.: Linear representations of finite groups, Springer, 1977.
Huppert, B.: Endliche Gruppen, I, Springer, 1967.
Knapp, A.W.: Representation theory of semisimple groups, Princeton Univ. Press, 1986.
Tits, J.: Tabellen zu den einfachen Lie Grupppen und ihren Darstellungen, Lecture notes in math., 40, Springer, 1967.
Warner, G.: Harmonic analysis on semisimple Lie groups, 1-2, Springer, 1972.
Bourbaki, N.: Elements of mathematics. Lie groups and Lie algebras, Addison-Wesley, 1975 (translated from the French).
Dixmier, J.: Enveloping algebras, North-Holland, 1977 (translated from the French).
Jacobson, N.: Lie algebras, Interscience, 1962.
Mil’ner, A.A.: ‘Maximal degree of irreducible Lie algebra representations over a field of positive characteristic’, Funct. Anal. Appl. 14, no. 2 (1980), 136–137. (Funkts. Anal. i Prilozhen. 14, no. 2(1980), 67-68)
Serre, J.-P.: Lie algebras and Lie groups, Benjamin, 1965 (translated from the French).
Théorie des algèbres de Lie. Topologie des groupes de Lie, Sem. S. Lie 1954/55, Secr. Math. Univ. Paris, 1955.
Zassenhaus, H.: ‘The representations of Lie algebras of prime characteristic’, Froc. Glasgow Math. Assoc. 2 (1954), 1–36.
Veĭsfeĭler, B. Yu. and Kats, V.G.: ‘Irreducible representations of Lie p-algebras’, Funct. Anal. Appl. 5, no. 2 (1971), 111–117. (Funkts. Anal. i Prilozhen. 5, no. 2 (1971), 28-36)
Jantzen, J.C.: ‘Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren’, Math. Z. 140, no. 1 (1974), 127–149.
Rudakov, A.N.: ‘On the representation of the classical Lie algebras in characteristic p’, Math. USSR Izv. 4 (1970), 741–749. (Izv. Akad. Nauk SSSR Ser. Mat. 34, no. 4 (1970), 735-743)
Humphreys, J.E.: Introduction to Lie algebras and representation theory, Springer, 1972.
Jantzen, J.C.: Einhüllende Algebren halbeinfacher Lie-Algebren, Springer, 1983.
Kleĭner, M.M.: ‘Partially ordered sets of finite type’, J. Soviet Math. 3 (1975), 607–615. (Zap. Nauchn. Sem. Leningr. Otdel. Mat. Inst. 28 (1972), 32-41)
Kleiner, M.M.: ‘On the exact representations of partially ordered sets of finite type’, J. Soviet Math. 3 (1975), 616–628. (Zap. Nauchn. Sem. Leningr. Otdel. Mat. Inst. 28 (1972), 42-60)
Nazarova, L.A.: ‘Partially ordered sets of infinite type’, Math. USSR Izv. 9, no. 5 (1975), 911–938. (Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 963-991 )
Clifford, A.H. and Preston, G.B.: The algebraic theory of semigroups, 1-2, Amer. Math. Soc, 1961-1967.
Vagner, V.V.: ‘Representations of ordered semi-groups’, Mat. Sb. 38, no. 2 (1956), 203–240 (in Russian).
Lyapin, E.S.: ‘Representations of semi-groups by partial mappings’, Mat. Sb. 52, no. 1 (1960), 589–596 (in Russian).
Shaĭn, B.M.: ‘Representations of semi-groups by binary relations’, Mat. Sb. 60, no. 3 (1963), 293–303 (in Russian).
McAlister, D.B.: ‘Representations of semigroups by linear transformations I’, Semi-group Forum 2, no. 3 (1971), 189–263.
McAlister, D.B.: ‘Representations of semigroups by linear transformations II’, Semi-group Forum 2, no. 4 (1971), 283–320.
Jönsson, B.: Topics in universal algebra, Springer, 1972.
Barut, A. and Raczka, R.: Theory of group representations and applications, 1-2, PWN, 1977.
Vilenkin, N. Ya.: Special functions and the theory of group representations, Amer. Math. Soc, 1968 (translated from the Russian).
Gel’fand, I.M., Graev, M.I. and Pyatetskiĭ-Shapiro, I.I.: Generalized functions, Saunders, 1969 (translated from the Russian).
Jaquet, E. and Langlands, R.: Automorphic forms on GL2, 1-2, Springer, 1970-1972.
Zhelobenko, D.P.: Compact Lie groups and their representations, Amer. Math. Soc, 1973 (translated from the Russian).
Zhelobenko, D.P.: Harmonic analysis of functions on semisimple complex Lie groups, Moscow, 1974 (in Russian).
Zhelobenko, D.P. and Shtern, A.I.: Representations of Lie groups, Moscow, 1983 (in Russian).
Kirillov, A.A.: Elements of the theory of representations, Springer, 1976 (translated from the Russian).
Klimyk, A.U.: Matrix elements and Clebsch — Gordan coefficients of group representations, Kiev, 1979 (in Russian).
Lang, S.: SL2(R), Addison-Wesley, 1975.
Naĭmark, M.A.: Normed rings, Reidel, 1984 (translated from the Russian).
Naĭmark, M.A.: Theory of group representations, Springer, 1982 (translated from the Russian).
Gaal, S.A.: Linear analysis and representation theory, Springer, 1973.
Gel’fand, I.M. (ed.): Lie groups and their representations, Hilger, 1975.
Mackey, G.W.: Unitary group representations in physics, probability and number theory, Benjaming/Cummings, 1978.
Carmona, J. and Vergne, M. (ed.): Non-commutative harmonic analysis, Lecture notes in math., 728, Springer, 1979.
Bondarenko, V.M. and Drozd, Yu. A.: ‘Representation type of finite groups’, J. Soviet Math. 20, no. 6 (1982), 2515–2528. (Zap. Nauchn. Sem. Leningr. Univ. 71 (1977), 24-41)
Kruglyak, S.A.: ‘Representations of algebras the square of whose radical equals zero’, J. Soviet Math. 3, no. 5 (1975), 629–636. (Zap. Nauchn. Sem. Leningr. Univ. 28(1972), 60-69)
Curtis, C.W. and Reiner, I.: Representation theory of finite groups and associative algebras, Interscience, 1962.
Nazarova, L.A.: ‘Representations of quivers of infinite type’, Math. USSR Izv. 7, no. 4 (1973), 749–792. (Izv. Akad. Nauk SSSR Ser. Mat. 37, no. 4 (1973), 752-791)
Fischbacher, U.: ‘Une nouvelle preuve d’un théorème de Nazarova et Roĭter’, C.R. Acad. Sci. Paris 300 (1984), 259–263.
Bautista, R., Gabriel, P., Roĭter, A. and Salmeron, L.: ‘Representation finite algebras and multiplicative bases’, Invent. Math. 81 (1985), 217–285.
Roĭter, A.V.: ‘Unbounded dimensionality of indecomposable representations of an algebra with an infinite number of indecomposable representations’, Math. USSR Izv. 2, no. 6 (1968), 1223–1230. (Izv. Akad. Nauk SSSR Ser. Mat. 32, no. 6 (1968), 1275-1282)
Dlab, V. and Ringel, C.: Indecomposable representations of graphs and algebras, Amer. Math. Soc, 1976.
Donovan, P. and Freislich, M.R.: The representation theory of finite graphs and associated algebras, Carleton Univ., 1974.
Gabriel, P.: ‘Unzerlegbare Darstellungen I’, Manuscripta Math. 6, no. 1 (1972), 71–103.
Auslander, M.: ‘Applications of morphisms determined by objects’, in R. Gordon (ed.): Representation Theory of Algebras, M. Dekker, 1978, pp. 245-327.
Auslander, M. and Reiten, I.: ‘Representation theory of Artin algebras III’, Comm. in Algebra (1975), 239-294.
Bautista, R.: ‘On algebras of strongly unbounded representation type’, Comment. Math. Helv. 60 (1985), 392–399.
Bongartz, K.: ‘A criterion for finite representation type’, Math. Ann. 269 (1984), 1–12.
Bongartz, K.: ‘Indécomposables are standard’, Comment. Math. Helv. 60 (1985), 400–410.
Bongartz, K. and Gabriel, P.: ‘Covering spaces in representation theory’, Invent. Math. 65 (1981), 381–387.
Drozd, Yu. A.: Tame and wild matrix problems’, in V. Dlab and P. Gabriel (eds.): Representation Theory II, Lecture notes in math., Vol. 832, Springer, 1980, pp. 242-258.
Dräxler, P.: ‘U-Fasersummen in darstellungsendlichen Algebren’, J. Algebra 113 (1988), 430–437.
Happel, D. and Vossieck, D.: ‘Minimal algebras of infinite representation type with preprojective component’, Manuscripta Math. 42 (1983), 221–243.
Happel, D., Preiser, U. and Ringel, C.M.: ‘Vinberg’s characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules’, in V. Dlab and P. Gabriel (eds.): Representation Theory II, Lecture notes in math., Vol. 832, Springer, 1980, pp. 280-294.
Nazarova, L.A. and RoTter, A.V.: Categorical matrix problems and the Brauer— Thrall conjecture, Kiev, 1973 (in Russian).
Ringel, C. M. and Tachikawa, H.: ‘QF-3 rings’, J. Reine Angew. Math. 272 (1975), 49–72.
Riedtmann, Chr.: ‘Algebren, Darstellungsköcher, Überlagerungen, und zurück’, Comment. Math. Helv. 55 (1980), 199–224.
Ringel, C. M.: Tame algebras and integral quadratic forms, Lecture notes in math., 1099, Springer, 1984.
Happel, D.: Triangulated categories in representation theory of finite dimensional algebras, London Math. Soc, 1988.
Kirillov, A.A.: Elements of the theory of representations, Springer, 1976 (translated from the Russian).
Plotkin, B.P.: Groups of automorphisms of algebraic systems, Wolters-Noordhoff, 1972 (translated from the Russian).
Markov, A.A.: ‘On an unsolvable problem concerning matrices’, Dokl. Akad. Nauk SSSR 78, no. 6 (1951), 1089–1092 (in Russian).
Markov, A.A.: Theory of algorithms, Israel Progr. Sci. Transi., 1961 (translated from the Russian). Also: Trudy Mat. Inst. Steklov. 42(1954).
Markov, A.A.: ‘On the problem of presenting matrices’, Z. Math. Logik und Grundl. Math. 4 (1958), 157–168 (in Russian). German abstract.
Nagornyĭ, N.M.: 6-th All-Union Congress on Math. Logic, Tbilisi, 1982, p. 124 (in Russian).
Paterson, M.S.: ‘Unsolvability in 3×3 matrices’, Stud, in Appl. Math. 49, no. 1 (1970), 105–107.
Weyl, H.: The classical groups, their invariants and representations, Princeton Univ. Press, 1946.
Zhelobenko, D.P.: Compact Lie groups and their representations, Amer. Math. Soc, 1973 (translated from the Russian).
Hamermesh, M.: Group theory and its application to physical problems, Addison-Wesley, 1962.
Carter, R.W. and Lustig, G.: ‘On the modular representations of the general linear and symmetric groups’, Math. Z. 136 (1974), 193–242.
Green, J.A.: Polynomial representations of GL n, Lecture notes in math., 830, Springer, 1980.
James, G. and Kerber, A.: The representation theory of the symmetric group, Addison-Wesley, 1981.
Feit, W.: The representation theory of finite groups, North-Holland, 1982.
Weyl, H.: The classical groups, their invariants and representations, Princeton Univ. Press, 1946.
Murnagan, F.D.: The theory of group representations, J. Hopkins Univ. Press, 1938.
Hamermesh, M.: Group theory and its application to physical problems, Addison-Wesley, 1962.
Curtis, C.W. and Reiner, I.: Representation theory of finite groups and associative algebras, Interscience, 1962.
James, G.: The representation theory of the symmetric groups, Springer, 1978.
Liulevicius, A.: ‘Arrows, symmetries, and representation rings’, J. Pure Appl. Algebra 19 (1980), 259–273.
Hazewinkel, M.: Formal rings and applications, Acad. Press, 1978.
Atiyah, M.F.: ‘Power operations in K-theory’, Quarterly J. Math. (2) 17 (1966), 165–193.
Knutson, D.: λ-rings and the representation theory of the symmetric group, Springer, 1973.
Zelevinsky, A.V.: Representations of finite classical groups, Springer, 1981.
Ravenel, D.C.: ‘The Hopf ring for complex cobordism’, J. Pure Appl. Algebra 9 (1977), 241–280.
Roman, S.: The umbral calculus, Acad. Press, 1984.
James, G. and Kerber, A.: The representation theory of the symmetric group, Addison-Wesley, 1981.
Robinson, G. de B.: Representation theory of the symmetric group, Univ. Toronto Press, 1961.
Green, J.A.: Polynomial representations of GLn, Lecture notes in math., 30, Springer, 1980.
Kirillov, A.A.: Elements of the theory of representations, Springer, 1976 (translated from the Russian).
Curtis, C.W. and Reiner, J.: Representation theory of finite groups and associative algebras, Interscience, 1962.
Jacobson, N.: Lie algebras, Interscience, 1962.
Théorie des algèbres de Lie. Topologie des groupes de Lie, Sém. S. Lie, Secr. Math. Univ. Paris, 1955.
Zhelobenko, D.P.: Compact Lie groups and their representations, Amer. Math. Soc, 1973 (translated from the Russian).
Cartan, E.: ‘Les tenseurs irréductibles et les groupes linéaires simples et semi-simples’, Bull. Sci. Math. 49 (1925), 130–152.
Harish-Chandra: ‘On some applications of the universal enveloping algebra of a semisimple Lie algebra’, Trans. Amer. Math. Soc. 70 (1951), 28–96.
Kargapolov, M.I. and Merzlyakov, Yu. I.: Fundamentals of the theory of groups, Springer, 1979 (translated from the Russian)
Robinson, D.J.S.: A course in the theory of groups, Springer, 1982.
Mal’tsev, A.I.: ‘Homomorphisms onto finite groups’, Uchen. Zap. Ivanovsk. Ped. Inst. 18 (1958), 49–60 (in Russian).
Golubov, E.A.: ‘Finitely approximable regular semi-groups’, Math. Notes 17, no. 3 (1975), 247–251. (Mat. Zam. 17, no. 3 (1975), 423-432)
Golubov, E.A. and Sapir, M.V.: ‘Varieties of finitely approximable semigroups’, Soviet Math. Dokl. 20, no. 4 (1979), 828–832. (Dokl Akad. Nauk SSSR 247, no. 5 (1979), 1037-1041)
Lallement, G.: ‘On nilpotency and residual finiteness in semigroups’, Pacific J. Math. 42, no. 3 (1972), 693–700.
Cohn, P.M.: Universal algebra, Reidel, 1981.
Blyth, T.S. and Janowitz, M.F.: Residuation theory, Pergamon, 1972.
Aĭzenberg, L.A. and Yuzhakov, A.P.: Integral representations and residues in multidimensional complex analysis, Transi. Math. Monographs, 58, Amer. Math. Soc, 1983 (translated from the Russian).
Berenstein, C. A., Gay, R. and Yger, A.: ‘Analytic continuation of currents and division problems’, Forum Math. (1989), 15-51.
Griffith, Ph. and Harris, J.: Principles of algebraic geometry, Wiley, 1978.
Passare, M.: ‘Residues, currents and their relation to ideals of holomorphic functions’, Math. Scand. 62 (1988), 75–152.
Federer, H.: Geometric measure theory, Springer, 1969.
Harvey, R.: ‘Holomorphic chains and their boundaries’, in R.O. Wells, jr. (ed.): Several Complex Variables, Proc. Symp. Pure Math., Vol. 30:1, Amer. Math. Soc., 1977, pp. 309-382.
Skoda, H.: ‘A survey of the theory of closed, positive currents’, in Y.-T. Siu (ed.): Complex Analysis of Several Variables, Vol. 41, Amer. Math. Soc, 1984, pp. 181-190.
Chirka, E.M.: Complex analytic sets, Kluwer, 1989 (translated from the Russian).
Markushevich, A.I.: Theory of functions of a complex variable, 1, Chelsea, 1977 (translated from the Russian).
Evgrafov, M.A.: Analytic functions, Saunders, 1966 (translated from the Russian).
Priwalow, I.I. [I.I. Privalov]: Einführung in die Funktionentheorie, 1-3, Teubner, 1958-1959 (translated from the Russian).
Shabat, B.V.: Introduction to complex analysis, 1-2, Moscow, 1985 (in Russian).
Springer, G.: Introduction to Riemann surfaces, Addison-Wesley, 1957.
Poincaré, H.: ‘Sur les résidues des intégrales doubles’, Acta Math. 9 (1887), 321–380.
Leray, J.: ‘Le calcule différentiel et intégral sur une variété analytique complexe (Problème de Cauchy, III)’, Bull. Soc. Math. France 87 (1959), 81–180.
Aĭzenberg, L.A. and Yuzhakov, A.P.: Integral representations and residues in multidimensional complex analysis. Amer. Math. Soc, 1983 (translated from the Russian).
Tsikh, A.K.: Multidimensional residues and its applications, Amer. Math. Soc, Forthcoming (translated from the Russian).
Griffiths, P.A.: ‘On the periods of certain rational integrals I’, Ann. of Math. (2) 90, no. 3 (1969), 460–495.
Egorichev, G.P.: Integral representation and the computation of combinatorial sums, Amer. Math. Soc, 1984 (translated from the Russian).
Griffiths, P.A. and Harris, J.: Principles of algebraic geometry, Wiley (Interscience), 1978.
Coleff, W.R. and Herrera, M.F.: Les courants residuals associés à une forme meromorphe, Lecture notes in math., 633, Springer, 1978.
Mitrinovic, D.S. and Keckic, J.D.: The Cauchy method of residues: theory and applications, Reidel, 1984.
Grothendieck, A.: ‘Sur quelques points d’algèbre homologique’, Tohoku Math. J. 9 (1957), 119–221.
Lang, S.: Algebra, Addison-Wesley, 1984.
Hartshorne, R.: Algebraic geometry, Springer, 1977.
André, M.: Méthode simpliciale en algèbre homologique et algèbre commutative, Lecture notes in math., 32, Springer, 1967.
Berthelot, P. and Ogus, A.: Notes on crystalline cohomology, Princeton Univ. Press, 1978.
Milne, J.S.: Etale cohomology, Princeton Univ. Press, 1980.
Cartan, H. and Eilenberg, S.: Homological algebra, Princeton Univ. Press, 1956.
MacLane, S.: Homology, Springer, 1963.
Godement, R.: Théorie des faisceaux, Hermann, 1964.
Abhyankar, S.S.: Resolution of singularities of embedded algebraic surfaces, Acad. Press, 1966.
Lipman, J.: ‘Introduction to resolution of singularities’, in R. Hartshorne (ed.): Algebraic Geometry, Arcata 1974, Proc. Symp. Pure Math., Vol. 29, Amer. Math. Soc, 1975, pp. 187-230.
Hironaka, H.: ‘Resolution of singulariies of an algebraic variety over a field of characteristic zero I, II’, Ann. of Math. 79 (1964), 109–326.
Riesz, F. and Szökefalvi-Nagy, B.: Functionals analysis, F. Ungar, 1955 (translated from the French).
Akhiezer, N.I. and Glazman, I.M.: Theory of linear operators in a Hilbert space, 1-2, F. Ungar, 1961-1963 (translated from the Russian).
Kantorovich, L.V. and Akilov, G.P.: Functionals analysis in normed spaces, Pergamon, 1964 (translated from the Russian).
Waerden, B.L. van der: Algebra, 1-2, Springer, 1967-1971 (translated from the German).
Yosida, K.: Functionals analysis, Springer, 1980.
Achiezer, N.I. [N.I. Akhiezer] and Glazman, I.M.: Theorie der linearen Operatoren im Hilbert Raum, Akad. Verlag, 1954 (translated from the Russian).
Kantorovich, L.V. and Akilov, G.P.: Functionals analysis in normed spaces, Pergamon, 1964 (translated from the Russian).
Riesz, F. and Szökevalfi-Nagy, B.: Leçons d’analyse fonctionelle, Akad. Kiado, 1952.
Yoshida, K.: Functionals analysis, Springer, 1978, p. 209ff.
Reed, M. and Simon, B.: Methods of modern mathematical physics, 1. Functionals analysis, Acad. Press, p. 188, 253.
Strelkov, S.P.: Introduction to the theory of oscillations, Moscow-Leningrad, 1951 (in Russian).
Arnol’d, V.I.: Ordinary differential equations, M.I.T., 1973 (translated from the Russian).
Bruno, A.D. [A.D. Bryuno]: Local methods in nonlinear differential equations, Springer, 1978 (translated from the Russian).
Bruno, A.D. [A.D. Bryuno]: ‘The analytic form of differential equations’, Trans. Moscow Math. Soc. 25 (1971), 131–288. (Trudy Moskov. Mat. Obshch. 25 (1971), 119-262)
Bruno, A.D. [A.D. Bryuno]: ‘The analytic form of differential equations’, Trans. Moscow Math. Soc. 26 (1972), 199–238. (Trudy Moskov. Mat. Obshch. 26 (1972), 199-239)
Arnol’d, V.I.: Mathematical methods of classical mechanics, Springer, 1978 (translated from the Russian).
Arnol’d, V.I.: Ordinary differential equations, M.I.T., 1973 (translated from the Russian).
Arnol’d, V.I. and Avez, A.: Ergodic problems of classical mechanics, Benjamin, 1968 (translated from the Russian).
Kurosh, A.G.: Higher algebra, Mir, 1972 (translated from the Russian).
Okunev, L.Y.: Higher algebra, Moscow-Leningrad, 1979 (in Russian).
Waerden, B.L. van der: Algebra, 1-2, Springer, 1967-1971 (translated from the German).
Hodge, W.V.D. and Pedoe, D.: Methods of algebraic geometry, 1-3, Cambridge Univ. Press, 1947-1954.
Lang, S.: Algebra, Addison-Wesley, 1984.
Bitsadze, A.V.: Equations of mathematical physics, Mir, 1980 (translated from the Russian).
Bers, L., John, F. and Schechter, M.: Partial differential equations. Interscience, 1964.
Vladimirov, V.S.: Equations of mathematical physics, Mir, 1984 (translated from the Russian).
Courant, R. and Hilbert, D.: Methods of mathematical physics. Partial differential equations, 2, Interscience, 1965 (translated from the German).
Pontryagin, L.S.: Ordinary differential equations, Addison-Wesley, 1962 (translated from the Russian).
Tikhonov, A.N. and Samarskiĭ, A.A.: Equations of mathematicalphysics, Pergamon, 1963 (translated from the Russian).
Borsuk, K.: Theory of retracts, PWN, 1967.
Shchepin, E.S.: ‘A finite-dimensional compact absolute neighborhood retract is metrizable’, Soviet Math. Doklady 18 (1977), 402–406. (Dokl. Akad. Nauk SSSR 233, no. 3 (1977), 304-307)
Mill, J. van: Infinite-dimensional topology, prerequisities and introduction, North-Holland, 1988.
Batchelor, G.K.: An introduction to fluid dynamics, Cambridge Univ. Press, 1967, Sect. 4.7.
Vishik, M.I. and Fursikov, A.V.: Mathematical problems of statistical hydromechanics, Kluwer, 1988, Chapts. 3; 4; 6 (translated from the Russian).
Landau, L.D. and Lifshitz, E.M.: Fluid mechanics, Pergamon, 1959 (translated from the Russian).
Rektorys, K.: Applicable mathematics, Iliffe, 1969, p. 135.
Finikov, S.P.: Projective-differential geometry, Moscow-Leningrad, 1937 (in Russian).
Finikov, S.P.: Theorie der Kongruenzen, Akademie-Verlag, 1959 (translated from the Russian).
Savelov, A.A.: Planar curves, Moscow, 1960 (in Russian).
Rashevskiĭ, P.K.: A course in differential geometry, Moscow, 1956 (in Russian).
Gomes Teixeira, F.: Traité des courbes, 1-3, Chelsea, reprint, 1971.
Riccati, J.: Opere, Treviso, 1758.
Kamke, E.: Differentialgleichungen. Lösungsmethoden und Lösungen, 1. Gewöhnliche Differentialgleichungen, Chelsea, reprint, 1971.
Erugin, N.P.: A reader for a general course in differential equations, Minsk, 1979 (in Russian).
Erugin, N.P.: Linear systems of ordinary differential equations with periodic and quasi-periodic coefficients, Acad. Press, 1966 (translated from the Russian).
Reid, W.T.: Riccati differential equations, Acad. Press, 1972.
Kalman, R., Falb, P. and Arbib, M.: Topics in mathematical system theory, McGraw-Hill, 1969.
Lions, J.-L.: Optimal control of systems governed by partial differential equations, Springer, 1971 (translated from the French).
Zakhar-Itkin, M.K.: ‘The matrix Riccati differential equation and the semi-group of linear fractional transformations’, Russian Math. Surveys 28, no. 3 (1973), 89–131. (Uspekhi Mat. Nauk 28, no. 3 (1973), 83-120)
Schneider, C.R.: ‘Global aspects of the matrix Riccati equation’, Math Syst. Theory 7, no. 3 (1973), 281–286.
Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Grossen, Springer, 1968.
Petrov, A.Z.: Einstein spaces, Pergamon, 1969 (translated from the Russian).
Hicks, N.: Notes on differential geometry, v. Nostrand, 1965.
Besse, A.L.: Einstein manifolds, Springer, 1987.
Ricci, G. and Levi-Civita. T.: ‘Méthodes de calcul différentiel absolu et leurs applications’, Math. Ann. 54 (1901), 125–201.
Rashewski, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Klingenberg, W.: Riemannian geometry, de Gruyter, 1982 (translated from the German).
Hicks, N.J.: Notes on differential geometry, v. Nostrand, 1965.
Kobayashi, S. and Nomizu, K.: Foundations of differential geometry, 1, Wiley (Interscience), 1963.
Ricci, G.: Atti R. Inst. Venelo 53, no. 2 (1903-1904), 1233–1239.
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Kobayashi, S. and Nomizu, K.: Foundations of differential geometry, 1, Wiley (Interscience), 1963.
Chern, S.S. and Osserman, R.: ‘Remarks on the Riemannian metrics of a minimal submanifold’, in E. Looijenga, D. Siersma and F. Takens (eds.): Geometry Symp. (Utrecht, 1980), Lecture notes in math., Vol. 894, Springer, 1981, pp. 49-90.
Richardson, L.F.: ‘The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stress in a masonry dam’, Philos. Trans. Roy. Soc. Ser. A 210 (1910), 307–357.
Bulirsh, R. and Stoer, J.: ‘Fehlerabschätzungen und Extrapolation mit rationaler Funktionen bei Verfahren vom Richardson-Typus’, Numer. Math. 6, no. 5 (1964), 413–427.
Joyce, D.C.: ‘Survey of extrapolation processes in numerical analysis’, SIAM Review 13, no. 4 (1971), 435–490.
Marchuk, G.I. and Shaĭdurov, V.V.: Difference methods and their extrapolations, Springer, 1983 (translated from the Russian).
Bakhvalov, N.S.: Numerical methods: analysis, algebra, ordinary differential equations, Mir, 1977 (translated from the Russian).
Hivie, T.: ‘Generalized Neville type extrapolation schemes’, BIT 9 (1979), 204–213.
Rickart, C.E.: ‘Banach algebras with an adjoint operation’, Ann. of Math. 47 (1946), 528–550.
Berberian, S.K.: Baer *-rings, Springer, 1972.
Kaplansky, I.: Rings of operators, Benjamin, 1968.
Markov, V.T., Mikhalev, A.V., Skornyakov, L.A. and Tuganbaev, A.A.: ‘Modules’, J. Soviet Math. 23, no. 6 (1983), 2642–2707. (Itogi Nauk. i Tekn. Algebra Topol. Geom. 19 (1981), 31-134)
Apostol, T.M.: Mathematical analysis, Blaisdell, 1957.
Riemann, B.: ‘Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe’, in Gesammelte math. Abhandlungen, Dover, reprint, 1957, pp. 227-264.
Wolff, J.: Fourier’sche Reihen, Noordhoff, 1931.
Riemann, B.: ‘Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe’, in Gesammelte math. Abhandlungen, Dover, reprint, 1957, pp. 227-264.
Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
Riemann, B.: ‘Über die Hypothesen, welche der Geometrie zugrunde liegen’, in Das Kontinuum und andere Monographien, Chelsea, reprint, 1973.
Efimov, N.V.: Higher geometry, MIR, 1980 (in Russian).
Rozenfel’d, B.A.: Non-Euclidean spaces, Moscow, 1969 (in Russian).
Kagan, V.F.: The foundations of geometry, 2, Moscow, 1956 (in Russian).
Bogomolov, S.A.: An introduction to Riemann’s non-Euclidean geometry, Moscow-Leningrad, 1934 (in Russian).
Helmholtz, H.: ‘Über die Tatsachen, die der Geometrie zum Grunde liegen’, in Wissenschaftliche Abhandlungen, Vol. II, 1883, pp. 618-639.
Coxeter, H.S.M.: Non-euclidean geometry, Univ. Toronto Press, 1965.
Bachmann, F.: Aufbau der Geometrie aus dem Spiegelungsbegriff, Springer, 1959.
Coxeter, H.S.M.: Introduction to geometry, Wiley, 1989.
Gray, J.: Ideas of space, Oxford, 1989, Chapt. 14.
Manning, H.P.: Introductory non-Euclidean geometry, New York, 1963, Chapt. III.
Veblen, O. and Young, J.W.: Projective geometry, II, Blaisdell, 1946, Chapt. VII.
Berger, M.: Geometry, II, Springer, 1987, Chapt. 19 (translated from the French).
Riemann, B.: Collected works, Dover, reprint, 1953.
Hilbert, D.: Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Chelsea, reprint, 1953.
Plemelj, J.: ‘Riemannsche Funktionenscharen mit gegebenen Monodromiegruppe’, Monatsh. Math. Phys. 19 (1908), 211–245.
Privalov, 1.1.: ‘On a boundary problem in analytic function theory’, Mat. Sb. 41, no. 4 (1934), 519–526 (in Russian). French abstract.
Muskhelishvili, N.I.: Singular integral equations, Wolters-Noordhoff, 1972, Chapt. 2 (translated from the Russian).
Gakhov, F.D.: Boundary value problems, Pergamon, 1966 (translated from the Russian).
Rodin, Yu. L.: The Riemann boundary problem on Riemann surfaces, Reidel, 1988 (translated from the Russian).
Riemann, B.: Gesammelte mathematische Werke, Dover, reprint, 1953.
Hurwitz, A.: ‘Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkte’, in Mathematische Werke, Vol. 1, Birkhäuser, 1932, pp. 321-383.
Hurwitz, A. and Courant, R.: Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, 1, Springer, 1964.
Nevanlinna, R.: Uniformisierung, Springer, 1967.
Lang, S.: Introduction to algebraic and Abelian functions, Addison-Wesley, 1972.
Hartshorne, R.: Algebraic geometry, Springer, 1977, Sect. IV.2.
Griffiths, P. and Harris, J.: Principles of algebraic geometry, Wiley, 1978, pp. 216-219.
Hasse, H.: ‘Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei eindlichem Konstantenkörper’, Reine Angew. Math. 172 (1935), 37–54.
Farkas, H.M. and Kra, I.: Riemann surfaces, Springer, 1980.
Ivic, A.: The Riemann zeta-function, Wiley, 1985.
Titchmarsh, E.G.: The theory of the Riemann zeta function, Clarendon Press, 1951.
Edwards, H.M.: Riemann’s zeta function, Acad. Press, 1974.
Heilbronn, H.: ‘Zeta-functions and L-functions’, in J.W.S. Cassels and A. Fröhlich (eds.): Algebraic number theory, Acad. Press, 1967, pp. 204-230.
Narkiewicz, W.: Elementary and analytic theory of algebraic numbers, Springer & PWN, 1990, Chapt. 7, §1.
Riemann, B.: ‘Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe’, in H. Weber (ed.): B. Riemann’s Gesammelte Mathematische Werke, Dover, reprint, 1953, pp. 227-271. (Original: Göttinger Akad. Abh. 13 (1868)).
Il’in, V.A. and Poznyak, E.G.: Fundamentals of mathematical analysis, 1-2, Mir, 1982 (translated from the Russian).
Kudryavtsev, L.D.: A course of mathematical analysis, 1-2, Moscow, 1988 (in Russian).
Nikol’skiĭ, S.M.: A course of mathematical analysis, 1-2, Mir, 1977 (translated from the Russian).
Shilov, G.E.: Mathematical analysis, 1-2, MIT, 1974 (translated from the Russian).
Pesin, I.N.: Classical and modern integration theories, Acad. Press, 1970 (translated from the Russian).
Stromberg, K.: An introduction to classical real analysis, Wadsworth, 1981.
Rudin, W.: Principles of mathematical analysis, McGraw-Hill, 1976.
Bitsadze, A.V.: Equations of mixed type, Moscow, 1959 (in Russian).
Courant, R. and Hilbert, D.: Methods of mathematical physics. Partial differential equations, 2, Interscience, 1965 (translated from the German).
Smirnov, V.I.: A course of higher mathematics, Addison-Wesley, 1964 (translated from the Russian).
Garabedian, P.R.: Partial differential equations, Wiley, 1963.
Borel, A. and Serre, J.-P.: ‘La théorème de Riemann — Roch’, Bull. Soc. Math. France 86 (1958), 97–136.
Manin, Yu. I.: ‘Lectures on the K-functor in algebraic geometry’, Russian Math. Surveys 24, no. 5 (1969), 1–89. (Uspekhi Mat. Nauk 24, no. 5 (1969), 3-86)
Hartshorne, R.: Algebraic geometry, Springer, 1977.
Hirzebruch, F.: Topological methods in algebraic geometry, Springer, 1978 (translated from the German).
Baum, P., Fulton, W. and MacPherson, R.: ‘Riemann — Roch for singular varieties’, Publ. Math. IHES 45 (1975), 101–145.
Baum, P., Fulton, W. and MacPherson, R.: ‘Riemann — Roch for topological K-theory and singular varieties’, Acta Math. 143, no. 3-4 (1979), 155–192.
Berthelot, P., et. al. (eds.): ‘Théorie des intersections et théorème de Riemann — Roch’, in Sem. Geom. Alg. 6, Lecture notes in math., Vol. 225, Springer, 1971.
Lang, S.: Algebraic number theory, Addison-Wesley, 1970.
Szpiro, K.:’ sem. sur les pinceaux arithmétiques: La conjecture de Mordell’, Astérisque 127 (1985).
Lavrent’ev, M.A. and Shabat, B.V.: Methoden der komplexen Funktionentheorie, Deutsch. Verlag Wissenschaft., 1967 (translated from the Russian).
Nehari, Z.: Conformai mapping, Dover, reprint, 1975.
Nirenberg, L., Webster, S. and Yang, P.: ‘Local boundary regularity of holomorphic mappings’, Comm. Pure Appl. Math. 33 (1980), 305–338.
Pinchuk, S.I. and Khasanov, S.V.: ‘Asymptotically holomorphic functions and their applications’, Math. USSR-Sb. 62, no. 2 (1989), 541–550. (Mat. Sb. 134 (176) (1987), 546-555; 576)
Carathéodory, C.: Theory of functions, 2, Chelsea, reprint, 1954.
Ahlfors, L.V.: Complex analysis, McGraw-Hill, 1979.
Rudin, W.: Lectures on the edge-of-the-wedge theorem, Amer. Math. Soc, 1971.
Nitsche, J.C.C.: Vorlesungen über Minimalflächen, Springer, 1975.
Shabat, B.V.: Introduction to complex analysis, 1-2, Moscow, 1976 (in Russian).
Fuks, B.A.: Introduction to the theory of analytic functions of several complex variables, Amer. Math. Soc, 1965 (translated from the Russian).
Ahlfors, L.V.: Complex analysis, McGraw-Hill, 1979.
Riemann, B.: ‘Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe’, in Gesammelte math. Abhandlungen, Dover, reprint, 1957, pp. 227-264.
Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
Zygmund, A.: Trigonometric series, 1-2, Cambridge Univ. Press, 1988.
Hardy, G.H.: Divergent series, Clarendon, 1949.
Zeller, K. and Beekman, W.: Theorie der Limitierungsverfahren, Springer, 1970.
Riemann, B.: Gesammelte mathematische Werke, Dover, reprint, 1953.
Markushevich, A.I.: The theory of functions of a complex variable, 1-2, Chelsea, 1977 (translated from the Russian).
Hurwitz, A. and Courant, R.: Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Springer, 1964.
Stoĭlov, S.: The theory of functions of a complex variable, 1-2, Moscow, 1962 (in Russian and Rumanian).
Stoilow, S.: Leçons sur les principes topologiques de la théorie des fonctions analytiques, Gauthier-Villars, 1938.
Springer, G.: Introduction to Riemann surfaces, Chelsea, reprint, 1981.
Nevanlinna, R.: Uniformisierung, Springer, 1967.
Schiffer, M. and Spencer, D.C.: Functionals of finite Riemann surfaces, Princeton Univ. Press, 1954.
Chebotarev, N.G.: The theory of algebraic functions, Moscow-Leningrad, 1948 (in Russian).
Volkovyskiĭ, L.I.: ‘Investigation of the type problem for a simply-connected Riemann surface’, Trudy Mat. Inst. Steklov. 34 (1950), 3–171 (in Russian).
Volkovyskiĭ, L.I.: ‘Contempory studies on Riemann surfaces’, Uspekhi Mat. Nauk 11, no. 5 (1956), 77–84 (in Russian).
Krushkal’, S.L.: Quasi-conformai mappings and Riemann surfaces, Winston & Wiley, 1979 (translated from the Russian).
Krushkal’, S.L., Apanasov, B.N. and Gusevskiĭ, N.A.: Kleinian groups and uniformization in examples and problems, Amer. Math. Soc., 1986 (translated from the Russian).
Vinberg, E.B. and Shvartsman, O.V.: ‘Riemann surfaces’, J. Soviet Math. 14, no. 1 (1980), 985–1020. (Itogi Nauk. i Tekhn. Algebra. Topol. Geom. 16(1978), 191-245)
Bers, L.: ‘Quasiconformal mappings and Teichmüller’s theorem’, in R. Nevanlinna, et al. (ed.): Analytic Functions, Princeton Univ. Press, 1960, pp. 89-119.
Ahlfors, L.: ‘The complex analytic structure of the space of closed Riemann surfaces’, in R. Nevanlinna, et al. (ed.): Analytic Functions, Princeton Univ. Press, 1960, pp. 45-66.
Bers, L.:’ spaces of Riemann surfaces’, in J. Todd (ed.): Proc. Internat. Congress Mathematicians Edinburgh, 1958, Cambridge Univ. Press, 1958, pp. 349-361.
Bers, L.: ‘Simultaneous uniformization’, Bull. Amer. Math. Soc. 66 (1960), 94–97.
Bers, L.: ‘Holomorphic differentials as functions of moduli’, Bull. Amer. Math. Soc. 67 (1961), 206–210.
Ahlfors, L.: ‘On quasiconformal mappings’, J. d’Anal. Math. 3 (1954), 1–58; 207-208.
Bers, L.: ‘Uniformization, moduli, and Kleinian groups’, Bull. London Math. Soc. 4 (1972), 257–300.
Bers, L.: ‘The moduli of Kleinian groups’, Russian Math. Surveys 29, no. 2 (1974), 88–102. (Uspekhi Mat. Nauk 29, no. 2 (1974), 86-102)
Klein, F.: Riemannschen Flächen, Springer, reprint, 1986.
Weyl, H.: The concept of a Riemann surface, Addison-Wesley, 1955 (translated from the German).
Ahlfors, L.V. and Sario, L.: Riemann surfaces, Princeton Univ. Press, 1974.
Pfluger, A.: Theorie der Riemannschen Flächen, Springer, 1957.
Sario, L. and Nakai, M.: Classification theory of Riemann surfaces, Springer, 1970.
Heins, M.: Hardy classes on Riemann surfaces, Springer, 1969.
Gunning, R.C.: Lectures on Riemann surfaces, Princeton Univ. Press, 1966.
Gunning, R.C.: Lectures on Riemann surfaces: Jacobi varieties, Princeton Univ. Press, 1972.
Forster, O.: Lectures on Riemann surfaces, Springer, 1981 (translated from the German).
Griffiths, P. and Harris, J.: Principles of algebraic geometry, Wiley (Interscience), 1978.
Griffiths, P.: Introduction to algebraic curves, Amer. Math. Soc., 1989.
Farkas, H.M. and Kra, I.: Riemann surfaces, Springer, 1980.
Behnke, H. and Sommer, F.: Theorie der analytische Funktionen einer komplexen Veränderlichen, Springer, 1976.
Cohn, H.: Conformai mapping on Riemann surfaces, Dover, reprint, 1980.
Behnke, H. and Thullen, P.: Theorie der Funktionen mehrerer komplexer Veränderlichen, Springer, 1970.
Osgood, W.: Lehrbuch der Funktionentheorie, 1-2, Chelsea, reprint, 1965.
Tsuji, M.: Potential theory in modern function theory, Chelsea, reprint, 1975.
Constantinescu, C. and Cornea, A.: Ideale Ränder Riemannscher Flächen, Springer, 1963.
Nevanlinna, R.: Uniformisierung, Springer, 1967.
Springer, G.: Introduction to Riemann surfaces, Chelsea, reprint, 1981.
Krushkal’, S.L.: Quasi-conformai mappings and Riemann surfaces, Winston & Wiley, 1979 (translated from the Russian).
Bers, L.: ‘Uniformization, moduli, and Kleinian groups’, Bull. London Math. Soc. 4 (1972), 257–300.
Schiffer, M. and Spencer, D.C.: Functionals of finite Riemann surfaces, Princeton Univ. Press, 1954.
Abikoff, W.: The real analytic theory of Teichmüller space, Springer, 1980.
Farkas, H.M. and Kra, I.: Riemann surfaces, Springer, 1980.
Krushkal’, S.L., Apanasov, B.N. and Guserkiĭ, N.A.: Kleinian groups and uniformization in examples and problems, Amer. Math. Soc., 1986 (translated from the Russian).
Lehto, O.: Univalent functions and Teichmüller spaces, Springer, 1986.
Gardiner, F.P.: Teichmüller theory and quadratic differentials, Wiley (Interscience), 1987.
Nag, S.: The complex analytic theory of Teichmüller spaces, Wiley (Interscience), 1988.
Schlichenmaier, M.: An introduction to Riemann surfaces, algebraic curves, and moduli spaces, Springer, 1989.
Rashewski, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Grossen, Springer, 1968.
Kobayashi, S. and Nomizu, K.: Foundations of differential geometry, Wiley (Interscience), 1969.
Hicks, N.J.: Notes on differential geometry, v. Nostrand, 1965.
Schouten, J.A. and Struik, D.J.: Einführung in die neueren Methoden der Differentialgeometrie, Noordhoff, 1924.
Spivak, M.: A comprehensive introduction to differential geometry, 1-5, Publish or Perish, 1979.
Klingenberg, W.: Riemannian geometry, de Gruyter, 1982 (translated from the German).
Eisenhart, L.P.: An introduction to differential geometry with the use of the tensor calculus, Princeton Univ. Press, 1947.
Schouten, J.A.: Ricci calculus, Springer, 1954 (translated from the German).
Riemann, B.: Gesammelte mathematischen Abhandlungen, Dover, reprint, 1953.
Priwalow, I.I. [I.I. Privalov]: Einführung in die Funktionentheorie, 1-3, Teubner, 1958-1959 (translated from the Russian).
Goluzin, G.M.: Geometric theory of functions of a complex variable, Amer. Math. Soc., 1969 (translated from the Russian).
Knopp, K.: Theorie und Anwendung der unendlichen Reihen, Springer, 1964. English translation: Blackie, 1951.
Rudin, W.: Principles of mathematical analysis, McGraw-Hill, 1976, pp. 75-78.
Chebotarev, N.G.: The theory of algebraic functions, Moscow-Leningrad, 1948, p. Chapt. 9 (in Russian).
Markushevich, A.I.: Introduction to the classical theory of Abelian functions, Moscow, 1979 (in Russian).
Krazer, A.: Lehrbuch der Thetafunktionen, Chelsea, reprint, 1970.
Conforto, F.: Abelsche Funktionen und algebraische Geometrie, Springer, 1956.
Griffiths, P.A. and Harris, J.E.: Principles of algebraic geometry, 1-2, Wiley, 1978.
Arbarello, E.: ‘Periods of Abelian integrals, theta functions, and differential equations of KdV type’, in A.M. Gleason (ed.): Proc. Internat. Congress Mathematicians, Berkely 1986, Vol. I, Armer. Math. Soc., 1987, pp. 623-627.
Mumford, D.: Tata lectures on theta, 1-2, Birkhäuser, 1983-1984.
Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Grossen, Springer, 1968.
Lichnerowicz, A.: Global theory of connections and holonomy groups, Noordhoff, 1976 (translated from the French).
Klingenberg, W.: Riemannian geometry, de Gruyter, 1982 (translated from the German).
Shabat, B.V.: Introduction to complex analysis, 2, Moscow, 1976 (in Russian).
Gunning, R. and Rossi, H.: Analytic functions of several complex variables, Prentice-Hall, 1965.
Hörmander, L.: An introduction to complex analysis in several variables, North-Holland, 1973.
Behnke, H. and Thullen, P.: Theorie der Funktionen mehrerer komplexer Veränderlichen, Springer, 1970, Chapt. VI. 2. Erweiterte Aufl.
Grauert, H. and Fritzsche, K.: Several complex variables, Springer, 1976 (translated from the German).
Riemann, B.: ‘Über die Hypothesen, welche der Geometrie zu Grunde liegen’, in Das Kontinuum und andere Monographien, Chelsea, reprint, 1973.
Rashewski, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Grossen, Springer, 1968.
Aleksandrov, A.D.: Die innere Geometrie der konvexen Flächen, Akademie-Verlag, 1955 (translated from the Russian).
Burago, Yu. D. and Zalgaller, V.A.: ‘Convex sets in Riemannian spaces of non-negative curvature’, Russian Math. Surveys 32, no. 3 (1977), 1–57. (Uspekhi Mat. Nauk 32, no. 3 (1977), 3-55)
Milnor, J.W.: Morse theory, Princeton Univ. Press, 1963.
Cartan, E.: Leçons sur la géométrie des espaces de Riemann, Gauthier-Villars, 1928.
Kulkarni, R.S.: ‘Curvature and metric’, Ann. of Math. 91, no. 2(1970), 311–331.
Wolf, J.A.: Spaces of constant curvature, Publish or Perish
O’Neill, B.: Semi-Riemannian geometry, Acad. Press, 1983.
Klingenberg, W.: Riemannian geometry, de Gruyter, 1982 (translated from the German).
Gallot, S., Hulin, D. and Lafontaine, J.: Riemannian geometry, Springer, 1987.
Boothby, W.: An introduction to differentiable manifolds and Riemannian geometry, Acad. Press, 1975.
Gromoll, D., Klingenberg, W. and Meyer, W.: Riemannsche Geometrie im Grossen, Springer, 1968.
Burago, Yu. D. and Zalgaller, V.A.: ‘Convex sets in Riemannian spaces of non-negative curvature’, Russian Math. Surveys 32, no. 3 (1977), 1–57. (Uspekhi Mat. Nauk 32, no. 3 (1977), 3-55)
Cheeger, J. and Ebin, D.: Comparison theorems in Riemannian geometry, North-Holland, 1975.
Research on the metric theory of surfaces, Moscow, 1980 (in Russian; translated from the English and the French).
Schoen, R. and Yau, S.-T.: ‘Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with non-negative scalar curvature’, Ann. of Math. 110 (1979), 127–142.
Toponogov, V.A.: ‘Extremal theorems for Riemann spaces with curvature bounded above I’, Sib. Math. J. 15, no. 6 (1974), 954–971. (Sibirsk. Mat. Zh. 15, no. 6 (1974), 1348-1371)
Gromov, M. and Lawson, H.B., jr.: ‘Spin and scalar curvature in the presence of a fundamental group I’, Ann. of Math. 111, no. 2 (1980), 209–230.
Buser, P. and Karcher, H.: ‘Gromov’s almost flat manifolds’, Astérique 81 (1981).
Wolf, J.: Spaces of constant curvature, Publish or Perish, 1977.
Goldberg, S.: Curvature and homology, Acad. Press, 1962.
Besse, A.L.: Manifolds all of whose geodesics are closed, Springer, 1978.
Thurston, W.: The geometry and topology of 3-manifolds, Princeton Univ. Press, 1978. Preprint.
Heintze, E. and Karcher, H.: ‘A general comparison theorem with applications to volume estimates for submanifolds’, Ann. Sci. Ecole Norm. Sup. 11, no. 4 (1978), 451–470.
Cheeger, J.: ‘Pinching theorems for a certain class of Riemannian manifolds’, Amer. J. Math. 91, no. 3 (1969), 807–834.
Min-Do and Ruh, E.: ‘Comparison theorems for compact symmetric spaces’, Ann. Sci. Ecole Norm. Sup. 12 (1979), 335–353.
Gray, A.: ‘Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula’, Topology 21, no. 2 (1982), 201–228.
Berger, M. and Gostiaux, B.: Differential geometry: manifolds, curves, and surfaces, Springer, 1988, Sect. 11.4 (translated from the French).
Klingenberg, W.: Riemannian geometry, W. de Gruyter, 1982, Chapt. 2.
Gallot, S., Hulin, D. and Lafontaine, J.: Riemannian geometry, Springer, 1987 (translated from the French).
Boothby, W.: An introduction to differentiable manifolds and Riemannian geometry, Acad. Press, 1975.
Greub, W., Halperin, S. and Vanstone, R.: Connections, curvature, and cohomology, 1-3, Acad. Press, 1972-1976.
Eisenhart, L.P.: Riemannian geometry, Princeton Univ. Press, 1949.
Rashewski, P.K. [P.K. Rashevskiĭ]: Riemannsche Geometrie und Tensoranalyse, Deutsch. Verlag Wissenschaft., 1959 (translated from the Russian).
Riemann, B.: ‘Über die Hypothesen, welche der Geometrie zuGrunde liegen’, in Das Kontinuum und andere Monographien, Chelsea, reprint, 1973.
O’Neill, B.: Elementary differential geometry, Acad. Press, 1966.
Aleksandrov, A.D.: Die innere Geometrie der konvexen Flächen, Akademie-Verlag, 1955 (translated from the Russian).
Aleksandrov, A.D.: ‘A theorem on triangles in metric space and certain applications’, Trudy Mat. Inst. Steklov. 38 (1951), 5–23 (in Russian).
Alexandroff, A.D. [A.D. Aleksandrov]: ‘Über eine Verallgemeinerung der Riemannschen Geometrie’, Schrift. Inst. Math. Deutsch. Akad. Wiss. 1 (1957), 33–84.
Berestovskiĭ, V.N.: ‘Introduction of a Riemann structure into certain metric spaces’, Sib. Math. J. 16, no. 4 (1975), 499–507. (Sibirsk. Mat. Zh. 16, no. 4 (1975), 651-662)
Nikolaev, I.G.: ‘Space of directions at a point in a space of curvature not greater than K’, Sib. Math. J. 19, no. 6 (1978). 944–948. (Sibirsk. Math. Zh. 19, no. 6 (1978), 1341-1348)
Nikolaev, I. G.: ‘Solution of Plateau’s problem in spaces of curvature not greater than K’, Sib. Math. J. 20, no. 2 (1979), 246–251. (Sibirsk. Mat. Zh. 20, no. 2 (1979), 345-353)
Reshetnyak, Yu. G.: ‘To the theory of spaces with curvature not greater than K’, Mat. Sb. 52, no. 3 (1960), 789–798 (in Russian).
Reshetnyak, Yu. G.: ‘Inextensible mappings in a space of curvature no greater than K’, Sib. Math. J. 9, no. 4 (1968), 683–689. (Sibirsk. Mat. Zh. 9, no. 4 (1968), 918-927)
Nikolaev, LG.: ‘Smoothness of the metric of spaces with two-sided bounded A.D. Aleksandrov curvature’, Sib. Math. J. 24, no. 2 (1983), 247–263. (Sibersk. Mat Zh. 24, no. 2 (1983), 114-132)
Berestovskiĭ, V.N.: ‘Spaces with bounded curvature and distance geometry’, Sib. Math. J. 27, no. 1 (1986), 8–18. (Sibersk. Mat. Zh. 27, no. 1 (1986), 11-25).
Rinow, W.: Die innere Geometrie der metrischen Räume, Springer, 1961.
Gromov, M.: Structures métriques pour les variétés riemanniennes, Cedec-Nathan, 1981.
‘Elie Cartan et les mathématiques d’aujourd’hui’, Astérisque (1985).
Pogorelov, A.V.: Intrinsic geometry of surfaces, Amer. Math. Soc., 1973 (translated from the Russian).
Busemann, H.: The geometry of geodesics, Acad. Press, 1955.
Kobayasi, S. and Nomizu, K.: Foundations of differential geometry, 1-2, Wiley, 1963-1968.
Wolf, J.: Spaces of constant curvature, Publish or Perish, 1977.
Helgason, S.: Differential geometry, Lie groups, and symmetric spaces, Acad. Press, 1978.
Berard Bergery, L.: ‘Sur le courbure des métriques riemanniennes invariantes des groupes de Lie et des espaces homogènes’, Ann. Sci. Ecole Norm. Sup. 11, no. 4 (1978), 545–576.
Berard Bergery, L.: ‘Les variétés riemanniennes simplement connexes de dimension impairé à courbure strictement positive’, J. Math. Pures Appl. 55 (1976), 47–67.
Jensen, G.R.: ‘Einstein metrics on principle fiber bundles’, J. Dif. Geom. 8 (1973), 599–614.
d’Atri, J.E. and Ziller, W.: ‘Naturally reductive metrics and Einstein metrics on compact Lie groups’, Mem. Amer. Math. Soc. 18 (1979), 1–72.
Azencott, R. and Wilson, E.N.: ‘Homogeneous manifolds with negative curvature II’, Mem. Amer. Math. Soc. 8 (1976), 1–102.
Manturov, O.V.: ‘Homogeneous Riemannian spaces with an irreducible rotation group’, Trudy Sem. Vektor, i Tenzor. Anal. 13 (1966), 68–145 (in Russian).
Wolf, J.: ‘The geometry and structure of isotropy irreducible homogeneous spaces’, Acta Math. 120 (1968), 59–148.
Besse, A.L.: Einstein manifolds, Springer, 1987.
Riesz, M.: ‘Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires’, Acta Math. 49 (1926), 465–497.
Hardy, G.H., Littlewood, J.E. and Pölya, G.: Inequalities, Cambridge Univ. Press, 1934.
Thorin, G.O.: ‘An extension of a convexity theorem due to M. Riesz’, K. Fysiogr. Saallskap. i Lund Forh. 8, no. 14 (1936).
Stein, E.M. and Weiss, G.: Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1975.
Marcinkiewicz, J.: ‘Sur l’interpolation d’opérateurs’, C. R. Acad. Sci. Paris 208 (1939), 1272–1273.
Kreĭn, S.K., Petunin, Yu. I. and Semenov, E.M.: Interpolation of linear opeators, Amer. Math. Soc., 1982 (translated from the Russian).
Triebel, H.: Interpolation theory, Springer, 1978.
Riesz, F.: ‘Sur les systèmes orthogonaux de fonctions’, C.R. Acad Sci. Paris 144 (1907), 615–619.
Fischer, E.: C.R. Acad. Sci. Paris 144 (1907), 1022–1024; 1148-1150.
Natanson, I.P.: Theory of functions of a real variable, 1-2, F. Ungar, 1955-1961 (translated from the Russian).
Kadison, R.V. and Ringrose, J.R.: Fundamentals of the theory of operator algebras, 1, Acad. Press, 1983.
Riesz, F.: ‘Ueber eine Verallgemeinerung der Parsevalschen Formel’, Math. Z. 18(1923), 117–124.
Riesz, M.: ‘Sur les fonctions conjuguées’, Math. Z. 27 (1927), 218–244.
Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
Zygmund, A.: Trigonometric series, 1-2, Cambridge Univ. Press, 1988.
Butzer, P.L. and Nessel, R.J.: Fourier analysis and approximation, 1, Birkhäuser, 1971, Chapt. 8.
Hausdorff, F.: ‘Eine Ausdehnung des Parsevalschen Satzes über Fourier-reihen’, Math. Z. 16 (1923), 163–169.
Stein, E.M. and Weiss, G.: Fourier analysis on Euclidean space, Princeton Univ. Press, 1975, Chapt. VI, §5.
Riesz, M.: ‘Formule d’interpolation pour la dérivée d’une polynôme trigonométrique’, C.R. Acad. Sci. Paris 158 (1914), 1152–1154.
Bernshteĭn, S.N.: Extremal properties of polynomials and best approximation of continuous functions of a real variable, 1, Moscow-Leningrad, 1937 (in Russian).
Nikol’skiĭ, S.M.: Approximation of functions of several variables and imbedding theorems, Springer, 1975 (translated from the Russian).
Riesz. M.: ‘Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome’, Jahresber. Deutsch. Math.-Ver. 23 (1914), 354–368.
Timan, A.F.: Theory of approximation of functions of a real variable, Pergamon, 1963, Chapt. 4 (translated from the Russian).
Zygmund, A.: Trigonometric series, 1-2, Cambridge Univ. Press, 1988, Chapt. X.
Frostman, O.: ‘Potentiel d’équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions’, Medd. Lunds Univ. Mat. Sem. 3 (1935), 1–118.
Riesz, M.: ‘Intégrales de Riemann — Liouville et potentiels’, Acata Sci. Math. Szeged 9 (1938), 1–42.
Landkof, N.S.: Foundations of modem potential theory, Springer, 1972.
Hayman, W. and Kennedy, P.: Subharmonic functions, Acad. Press, 1976.
Bliedtner, J. and Hansen, W.: Potential theory. An analytic and probabilistic approch to balayage, Springer, 1986.
Schulze, B.W. and Wildenhain, G.: Methoden der Potentialtheorie für elliptische Differentialgleichungen beliebiger Ordnung, Birkhäuser, 1977.
Stein, E.M.: Singular integrals and differentiability properties of functions, Princeton Univ. Press, 1970.
Carlesson, L.: Selected problems on exceptional sets, v. Nostrand, 1967.
Bary, N.K. [N.K. Bari]: A treatise on trigonometric series, Pergamon, 1964 (translated from the Russian).
Zygmund, A.: Trigonometric series, 1-2, Cambridge Univ. Press, 1988.
Riesz, F.:’ sur la décomposition des opérations fonctionelles linéaires’, in Atti del Congr. Int. dei Math., Vol. 3, Bologna, 1930, pp. 143-148.
Luxemburg, W. and Zaanen, A.: Riesz spaces, I, North-Holland, 1971.
Vulikh, B.Z.: Introduction to the theory of partially ordered spaces, Wolters-Noordhoff, 1967 (translated from the Russian).
Zaanen, A.C.: Riesz spaces, II, North-Holland, 1983.
Schaefer, H.H.: Banach lattices and positive operators, Springer, 1974.
Jonge, E. de and Rooy, A.C.M. van: Introduction to Riesz spaces, Tracts, 8, Math. Centre, 1977.
Birkhoff, G.: Lattice theory, Colloq. Publ., 25, Amer. Math. Soc., 1973.
Kantorovich, B.Z., Vulikh, B.Z. and Pinsker, A.G.: Functionals analysis in partially ordered spaces, Moscow, 1950 (in Russian).
Freudenthal, H.: ‘Teilweise geordneten Moduln’, Proc. Royal Acad. Sci. Amsterdam 39 (1936), 641–651.
Nakano, H.: Modern spectral theory, Maruzen, 1950.
Riesz, M.: ‘Une méthode de sommation équivalente à la méthode des moyennes arithmétique’, C.R. Acad. Sci. Paris 152 (1911), 1651–1654.
Riesz, F.: ‘Sur la sommation des séries de Dirichlet’, C.R. Acad Sci. Paris 149 (1909), 18–21.
Hardy, G.H. and Riesz, M.: The general theory of Dirichlet series, Cambridge Univ. Press, 1915.
Hardy, G.H.: Divergent series, Clarendon Press, 1949.
Zeller, K. and Beekman, W.: Theorie der Limitierungsverfahren, Springer, 1970.
Bari, N.K.: ‘Sur les bases dans l’espace de Hilbert’, Dokl. Akad. Nauk SSSR 54 (1946), 379–382.
Bari, N.K.: ‘Biorthogonal systems and bases in Hilbert space’, Uchen. Zap. Moskov. Gos. Univ. 148, no. 4 (1951), 69–107 (in Russian).
Gohberg, I.C. [I. Ts. Gokhberg] and Kreĭn, M.G.: Introduction to the theory of linear nonselfadjoint operators, Amer. Math. Soc., 1969 (translated from the Russian).
Gaposhkin, V.F.: ‘Lacunary series and independent functions’, Russian Math. Surveys 21, no. 6 (1966), 1–82. (Uspekhi Mat. Nauk 21, no. 6 (1966), 3-82)
Riesz, F.: ‘Sur les fonctions sous harmoniques et leur rapport à la théorie du potentiel I’, Acta Math. 48 (1926), 329–343.
Riesz, F.: ‘Sur les fonctions sous harmoniques et leur rapport à la théorie du potentiel II’, Acta Math. 54 (1930), 321–360.
Riesz, F.: ‘Ueber die Randwerte einer analytischer Funktion’, Math. Z. 18 (1923), 87–95.
Privalov, I.I.: Subharmonic functions, Moscow-Leningrad, 1937 (in Russian).
Priwalow, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktionen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).
Hayman, W.K. and Kennedy, P.B.: Subharmonic functions, Acad. Press, 1976.
Asimow, L. and Ellis, A.J.: Convexity theory and its applications in functional analysis, Acad. Press, 1980.
Constantinescu, C. and Cornea, A.: Potential theory on harmonic spaces, Springer, 1972.
Riesz, F. and Riesz, M.: ‘Ueber die Randwerte einer analytischen Funktion’, in G. Mittag-Leftier (ed.): 4th Congress Math. Scand, Almqvist & Wiksells, 1920, pp. 27-44.
Privalov, I.I.: The Cauchy integral, Saratov, 1918 (in Russian).
Priwalow, I.I. [I.I. Privalov]: Randeigenschaften analytischer Funktionen, Deutsch. Verlag Wissenschaft., 1956 (translated from the Russian).
Brummelhuis, R.G.M.: ‘An F. and M. Riesz theorem for bounded symmetric domains’, Ann. Inst. Fourier 37 (1987), 139–150.
Duren, P.L.: Theory of H p spaces, Acad. Press, 1970.
Garnett, J.: Bounded analytic functions, Acad. Press, 1981.
Koosis, P.: Introduction to H p spaces, Cambridge Univ. Press, 1980.
Rudin, W.: Function theory in the unit ball of C n, Springer, 1980.
Rudin, W.: Real and complex analysis, McGraw-Hill, 1966.
Gel’fand, I.M. and Shilov, G.E.: Some problems in the theory of differential equations, Moscow, 1958 (in Russian).
Gel’fand, I.M. and Vilenkin, N. Ya.: Generalized functions. Applications of harmonic analysis, 4, Acad. Press, 1964 (translated from the Russian).
Berezanskiy, Yu. M. [Yu. M. Berezanskiĭ]: Expansion in eigenfunctions of selfadjoint operators, Amer. Math. Soc., 1968 (translated from the Russian).
Pontryagin, L.S.:’ smooth manifolds and their application in homotopy theory’, Trudy Mat. Inst. Steklov. 45 (1955) (in Russia)
Milnor, J.W.: Toplogy from the differentiale viewpoint, Univ. Press of Virginia, 1965.
Milnor, J.W.: ‘A survey of cobordism theory’, L’Enseign. Math. 8 (1962), 16–23.
Thom, R.: ‘Quelque propriétés globales des variétés différentiables’, Comm. Math. Helvet. 28 (1954), 17–28.
Dieudonné, J.: A history of algebraic and differential topology 1900–1960, Birkhäuser, 1989.
Dodson, C.T.J.: Categories, bundles, and spacetime topology, Kluwer, 1988, p. 94ff.
Hirsch, M.W.: Differential topology, Springer, 1976, p. 98.
Clifford, A.H. and Preston, G.B.: The algebraic theory of semigroups, 1-2, Amer. Math. Soc., 1961-1967.
Kokorin, A.I. and Kopytov, V.M.: Linearly ordered groups, Moscow, 1972 (in Russian).
Mura, R.B. and Rhemtulla, A.: Orderable groups, M. Dekker, 1977.
Anderson, M. and Feil, T.: Lattice ordered groups. An introduction, Reidel, 1988, p. 35; 38ff.
Glass, A.M.W. and Holland, W.C.: Lattice ordered groups. Advances and techniques, Kluwer, 1989.
Powell, W.B.: ‘Universal aspects of the theory of latticeordered groups’, in J. Martinez (ed.): Ordered Algebraic Structures, Kluwer, 1989, pp. 11-50.
Darnell, M.R.: ‘Recent results on the free lattice ordered group over a right-orderable group’, in J. Martinez (ed.): Ordered Algebraic Structures, Kluwer, 1989, pp. 51-57.
Täte, J.: ‘Rigid analytic spaces’, Invent. Math. 12 (1971), 257–289.
Bourbaki, N.A.: Variétés différentielles et analytique. Fascicule de résultats, Éléments de mathématique, Hermann, 1967-1971, Fasc. XXXIII (Par. 1-7); Fasc. XXXVI (Par. 8-15).
Serre, J.-P.: Lie algebras and Lie groups, Benjamin, 1965.
Serre, J.-P.: Algèbres de Lie semi-simples complexes, Benjamin, 1966.
Housel, C.: Espaces analytiques rigides, Sém. Bourbaki (1966/67), Exp. 32, Benjamin, 1968.
Mumford, D.: ‘An analytic construction of degenerating curves over complete local rings’, Compos. Math. 24, no. 2 (1972), 129–174.
Mumford, D.: ‘An analytic construction of degenerating abelian varieties over complete rings’, Compos. Math. 24, no. 2 (1972), 239–272.
Efimov, N.V.: ‘Qualitative problems of the theory of deformation of surfaces’, Uspekhi Mat. Nauk 3, no. 2 (1948), 47–158 (in Russian).
Pogorelov, A.V.: Extrinsic geometry of convex surfaces, Amer. Math. Soc., 1973 (translated from the Russian).
Cohn-Vossen, S.E.: Some problems of differential geometry in the large, Moscow, 1959 (in Russian).
Vekua, I.N.: Generalized analytic functions, Pergamon, 1962 (translated from the Russian).
Aleksandrov, A.D.: Konvexe Polyeder, Akademie-Verlag, 1958 (translated from the Russian).
Fomenko, V.T.: ‘Single-valued determination of closed surfaces of genus p≥1 in a space of constant curvature’, Math. Notes 16, no. 3 (1974), 852. (Mat. Zametki 16, no. 3 (1974), 441-445)
Huck, H., Roitzsch, R., Simon, U., Vortisch, W., Walden, R., Wegner, B. and Wendland, W.: Beweismethoden der Differentialgeometrie im Grossen, Lecture notes in math., 335, Springer, 1973.
Lang, S.: Algebra, Addison-Wesley, 1974.
Bourbaki, N.: Algèbre, Eléments de mathématiques, 2, Masson, 1981, Chapts. 4; 5; 6.
Hilbert, D.: ‘Ueber die vollen Invariantensysteme’, Math. Ann. 42 (1893), 313–373.
Hilbert, D.: ‘Ueber die Theorie der algebraischen Formen’, Math. Ann. 36 (1890), 473–534.
Suslin, A.A.: ‘Projective modules over a polynomial ring are free’, Soviet Math. Dokl. 17, no. 4 (1976), 1160–1164. (Dokl. Akad. Nauk SSSR 229 (1976), 1063-1066)
Quillen, D.: ‘Projective modules over polynomial rings’, Invent. Math. 36 (1976), 167–171.
Curtis, C.W. and Reiner, I.: Methods of representation theory, II, Wiley (Interscience), 1987.
Roby, N.: ‘Les algèbres à puissances divisées’, Bull. Soc. Math. France 89 (1965), 75–91.
Hazewinkel, M.: Formal groups and applications, Acad. Press, 1978.
Cartier, P.: ‘Exemples d’hyperalgèbres’, in Sem. S. Lie 1955/56, Vol. 3, Secr. Math. Univ. Paris, 1957.
Thomas, E.: The generalized Pontryagin cohomology operations and rings with divided powers, Amer. Math. Soc., 1957.
Eilenberg, S. and MacLane, S.: ‘On the groups H(π, n), II’, Ann. of Math. 60 (1954), 49–189.
Kurosh, A.G.: Lectures on general algebra, Chelsea, 1963 (translated from the Russian).
Jacobson, N.: The theory of rings, Amer. Math. Soc., 1943.
Kurosh, A.G.: Lectures on general algebra, Chelsea, 1963 (translated from the Russian).
Shafarevich, I.R.: Basic algebraic geometry, Springer, 1977 (translated from the Russian).
Hartshorne, R.: Algebraic geometry, Springer, 1977.
Kurosh, A.G.: Lectures on general algebra, Chelsea, 1963 (translated from the Russian).
Hilton, P.J. and Ledermann, W.: ‘Homology and ringoids. I’, Proc. Cambridge Phil. Soc. 54 (1958), 156–167.
Hilton, P. J. and Ledermann, W.: ‘Homology and ringoids. II’, Proc. Cambridge Phil. Soc. 55 (1959), 149–164.
Hilton, P. J. and Ledermann, W.: ‘Homology and ringoids. Ill’, Proc. Cambridge Phil. Soc. 56 (1960), 1–12.
Bourbaki, N.: Eléments d’histoire des mathématiques, Hermann, 1960.
Bourbaki, N.: Eléments de mathématiques. Algèbre: Polynômes; Corps commutatives; Groupes et corps ordonnés, Masson, 1981, Chapts. 4-6.
Bourbaki, N.: Elements of mathematics. Algebra: Algebraic structures. Linear algebra, 1, Addison-Wesley, 1974, Chapt.l;2 (translated from the French).
Bourbaki, N.: Elements of mathematics. Commutative algebra, Addison-Wesley, 1972 (translated from the French).
Jacobson, N.: The theory of rings, Amer. Math. Soc., 1943.
Jacobson, N.: Structure of rings, Amer. Math. Soc., 1956.
Jacobson, N.: Lie algebras, Interscience, 1962.
Zariski, O. and Samuel, P.: Commutative algebra, 1-2, Springer, 1975.
Atiyah, M. and Macdonald, LG.: Introduction to commutative algebra, Addison-Wesley, 1969.
Herstein, I.: Noncommutative rings, Math. Assoc. Amer., 1968.
Kurosh, A.G.: Higher algebra, Mir, 1972 (translated from the Russian).
Lang, S.: Algebra, Addison-Wesley, 1974.
Waerden, B.L. van der: Algebra, 1-2, Springer, 1967-1971 (translated from the German).
Pontryagin, L.S.: Topological groups, Princeton Univ. Press, 1958 (translated from the Russian).
Naĭmark, M.A.: Normed rings, Reidel, 1984 (translated from the Russian).
Faith, C.: Algebra: rings, modules and categories, 1, Springer, 1973.
Rowen, L.: Theory of rings, I-II, Acad. Press, 1988.
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Skornyakov, L.A. et al. (1995). R. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3791-9_6
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