References
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S. M. Nikol’skii, “Asymptotic Behavior of the Residual in the Approximation of Lipschitz Functions by Fejer Sums,” Izv. Akad. Nauk SSSR, Ser. Mat. 4, 501–508 (1940).
S. M. Nikol’skii, “Some Methods for Approximation by Trigonometric Sums,” Izv. Akad. Nauk SSSR, Ser. Mat. 4, 509–520 (1940).
S. M. Nikol’skii, “Asymptotic Estimate of the Residual in Approximation by Interpolation Trigonometric Polynomials,” Dokl. Akad. Nauk SSSR 31, 215–218 (1941).
S. M. Nikol’skii, “On a Functional Inequality,” Nauchn. Zap. Dnepropetrovsk. Univ. 25, 41–43 (1941).
S. M. Nikol’skii, “Linear Equations in Linear Normed Spaces,” Izv. Akad. Nauk SSSR, Ser. Mat. 7(3), 147–166 (1943).
S. M. Nikol’skii, Approximation of Periodic Functions by Trigonometric Polynomials, Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 15 (1945)).
S. M. Nikol’skii, “Approximation of Functions by Trigonometric Polynomials on Average,” Izv. Akad. Nauk SSSR, Ser. Mat. 10(3), 207–256 (1946).
S. M. Nikol’skii, “On the Best Approximation of Lipschitz Functions by Polynomials,” Izv. Akad. Nauk SSSR, Ser. Mat. 10, 295–322 (1946).
S. M. Nikol’skii, “Interpolation and the Best Approximation of Differentiable Periodic Functions by Trigonometric Polynomails,” Izv. Akad. Nauk SSSR, Ser. Mat. 10, 393–410 (1946).
S. M. Nikol’skii, “On the Best Approximation of the Function (a − x)2 by Polynomials on Average,” Izv. Akad. Nauk SSSR, Ser. Mat. 11, 139–180 (1947).
S. M. Nikol’skii, “Linear Summation Methods for Fourier Series,” Izv. Akad. Nauk SSSR, Ser. Mat. 12, 259–278 (1948).
S. M. Nikol’skii, “Polynomial Approximation of Functions of Real Variable,” in Mathematics in the USSR over 30 Years (Moscow, Gostekhizdat, 1948), pp. 288–318.
S. M. Nikol’skii, “Fourier Series of Functions with a Derivative of Bounded Variation,” Izv. Akad. Nauk SSSR, Ser. Mat. 13, 513–532 (1949).
S. M. Nikol’skii, “On Estimates of Approximations by Quadrature Formulas,” Usp. Mat. Nauk 5(2), 165–177 (1950).
S. M. Nikol’skii, “On the Best Approximation of Differentiable Functions by Polynomials,” Acta Sci. Math. (Szeged) 12, 185–197 (1950).
S. M. Nikol’skii, “Inequalities for Entire Functions of Finite Degree and Application to the Theory of Differentiable Functions of Several Variables,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 38, 244–278 (1951).
S. M. Nikol’skii, “Quadrature Formulas,” Izv. Akad. Nauk SSSR, Ser. Mat. 16, 181–196 (1952).
S. M. Nikol’skii, “On the Solution of a Polyharmonic Equation by the Variational Method,” Dokl. Akad. Nauk SSSR 88, 409–411 (1953).
S. M. Nikol’skii, “Properties of Some Classes of Functions of Several Variables on Differentiable Manifolds,” Mat. Sb. 35(2), 247–266 (1954).
S. M. Nikol’skii, “The Dirichlet Problem for a Circle and Half-Space,” Mat. Sb. 35(2), 247–266 (1954).
S. M. Nikol’skii, “Properties of Some Classes of Functions of Several Variables on Differentiable Manifolds and Their Application to Variational Problems,” Acta Math. Acad. Sci. Hung. 5, 61–70 (1954).
S. M. Nikol’skii, “On the Extension of Functions of Several Variables with the Preservation of Differentiable Properties,” Mat. Sb. 40(2), 243–268 (1956).
S. M. Nikol’skii and M. A. Lavrent’ev, “Analysis” in Mathematics: Its Scope, Methods, and Importance (Akad. Nauk SSSR, Moscow, 1956), Vol. 1, pp. 79–179 (translated into English, 1963).
S. M. Nikol’skii, “Approximation of Functions,” in Mathematics, Its Scope, Methods, and Importance (Akad. Nauk SSSR, Moscow, 1956), Vol. 2, pp. 285–322 (translated into English, 1963).
S. M. Nikol’skii, “One Variational Problem of Hilbert,” Dokl. Akad. Nauk SSSR 117, 573–575 (1957).
S. M. Nikol’skii, “Boundary Properties of Functions Defined on a Domain with Corner Points,” Mat. Sb. 40, 303–318 (1956).
S. M. Nikol’skii, “Boundary Properties of Functions Defined on a Domain with Corner Points: Harmonic Functions on Rectangular Domains,” Mat. Sb. 43, 127–144 (1957).
S. M. Nikol’skii, “Embedding Theorem for Functions with Partial Derivatives Considered in Various Metrics,” Izv. Akad. Nauk SSSR, Ser. Mat. 22, 599–630 (1958).
S. M. Nikol’skii, “Hilbert Variational Problem,” Izv. Akad. Nauk SSSR, Ser. Mat. 22, 599–630 (1958).
S. M. Nikol’skii, “Boundary Properties of Functions Defined on a Domain with Corner Points: Connection with the Polyharmonic Problem,” Mat. Sb. 45, 181–194 (1958).
S. M. Nikol’skii, Quadrature Formulas (Moscow, Fizmatgiz, 1958) (translated into English, 1964, 1966; into Romanian, 1964).
S. M. Nikol’skii, “Some Properties of Differential Functions Defined on an n-Dimensional Open Set,” Izv. Akad. Nauk SSSR, Ser. Mat. 23, 213–242 (1959).
S. M. Nikol’skii, “An Estimate of Functions with a Finite Dirichlet Integral and Application to Boundary Value Problems,” Izv. Akad. Nauk SSSR, Ser. Mat. 23, 677–696 (1959).
S. M. Nikol’skii, “A Boundary Estimate for Harmonic Function in an n-Dimensional Domain,” Sib. Mat. Zh. 1, 78–87 (1960).
S. M. Nikol’skii, “On Uniform Differential Properties of Analytic Functions in a Strip,” Mathematica 2(1), 149–157 (1960).
S. M. Nikol’skii, “Some Issues of Approximation of Functions by Polynomials,” in Proceedings of International Congress of Mathematicians in Amsterdam 1954 (Fizmatgiz, Moscow, 1961), pp. 259–281 [in Russian].
S. M. Nikol’skii, “On Inequalities between Partial Derivatives,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 64, 147–164 (1961).
S. M. Nikol’skii, “Theorems on Embedding, Extension, and Approximation of Differentiable Functions of Several Variables,” Usp. Mat. Nauk 16(5), 63–114 (1961) (“Series of Papers Concerning Theorems on Embedding, Extension, and Approximation of Differentiable Functions of Several Variables,” Rev. Roum. Math. Pures Appl. 6 (2), 209–258 (1961)).
S. M. Nikol’skii and L. D. Kudryavtsev, “Embedding Theorems and Application to the Solution of Elliptic Equations,” in “Certain Problems in Mathematics and Mechanics: Dedicated to Academician M. A. Lavrent’ev on the Occasion of His Sixtieth Birthday” (Sib. Otd. Akad. Nauk SSSR, Novosibirsk, 1961) pp. 87–109 [in Russian].
S. M. Nikol’skii, “Proof of the Uniqueness of a Classical Solution to the Dirichlet Boundary Value Problem for a General Linear Partial Differential Equation in a Convex Bounded Domain,” Izv. Akad. Nauk SSSR, Ser. Mat. 27, 1113–1134 (1963).
S. M. Nikol’skii, “On Stable Boundary Values of a Differentiable Function of Several Variables,” Mat. Sb. 61, 224–252 (1963).
S. M. Nikol’skii, “Variational Problem,” Mat. Sb. 62, 53–75 (1963).
S. M. Nikol’skii, “Functions with a Dominating Mixed Derivative Satisfying a Multiple Hölder Condition,” Sib. Mat. Zh. 4, 1342–1364 (1963).
S. M. Nikol’skii and P. I. Lizorkin, Classification of Differentiable Functions on the Basis of Spaces with Dominating Mixed Derivative,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 77, 143–167 (1965).
S. M. Nikol’skii, J.-L. Lions, and P. I. Lizorkin, “Integral Representation and Isomorphism Properties of Some Classes of Functions,” Ann. Scuola Norm. Super. Pisa Ser. 3 19(2), 127–178 (1965).
S. M. Nikol’skii, Quadrature Formulae (U.K. Atomic Energy Authority. Res. Group, Harwell, Berkshire, 1966) (AERE Translations, Vol. 1055) (Translated from the Russian Edition of 1958).
S. M. Nikol’skii, “Embedding Theorem for Classes of Generalized Functions,” Sib. Mat. Zh. 9, 1107–1126 (1968).
S. M. Nikol’skii, “Theory of Approximation of Functions by Polynomials,” in History of Russian Mathematics (Naukova Dumka, Kiev, 1968), Vol. 3, pp. 568–588 [in Russian].
S. M. Nikol’skii and L. D. Kudryavtsev, “Theory of Differential Functions of Several Variables (Embedding Theorems),” in History of Russian Mathematics (Naukova Dumka, Kiev, 1968), Vol. 3, pp. 588–607 [in Russian].
S. M. Nikol’skii and P. I. Lizorkin, “Compactness of the Set of Differentiable Functions,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 105, 168–177 (1969).
S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems (Nauka, Moscow, 1969) (translated into English, 1975).
S. M. Nikol’skii, Course of Mathematical Analysis (Nauka, Moscow, 1973), 2 vols.
S. M. Nikol’skii, Quadrature Formulas, 2nd ed. with supplements by N. P. Korneichuk (Nauka, Moscow, 1974).
S. M. Nikol’skii, Approximation of Function of Several Variables and Imbedding Theorems (Springer-Verlag, Berlin, 1975) (Translated from the Russian Edition of 1969).
S. M. Nikol’skii, O. V. Besov, V. P. Il’in, Integral Representations of Functions and Embedding Theorems (Nauka, Moscow, 1975) (translated into English, 1978, 1979).
S. M. Nikol’skii, Course of Mathematical Analysis, 2nd Ed., updated (Nauka, Moscow, 1975), 2 vols. (Translated into Latvian, 1976, 1977; English, 1977; Spanish, 1979).
S. M. Nikol’skii, “An Embedding Theorem for Functions of Upper Classes,” in Problems in Mathematics, Physics, and Computational Mathematics (Nauka, Moscow, 1977), pp. 254–264.
S. M. Nikol’skii, Approximation of Functions of Several Variables and Embedding Theorems, 2nd ed., updated (Nauka, Moscow, 1977).
S. M. Nikol’skii, O. V. Besov, and V. P. Il’in, Integral Representations of Functions and Imbedding Theorems (Wiley, New York, 1978), Vol. 1 (Translated from the Russian Edition of 1975).
S. M. Nikol’skii, “Variational Problem for an Elliptic Equation with Degeneration on the Boundary,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 150, 212–238 (1979).
S. M. Nikol’skii, O. V. Besov, and V. P. Il’in, Integral Representations of Functions and Imbedding Theorems (Wiley, New York 1979), Vol. 2 (Translated from the Russian Edition of 1975).
S. M. Nikol’skii, Quadrature Formulas, 3rd ed. with supplement by N. P. Korneichuk (Nauka, Moscow, 1979) (translated into English, 1990).
S. M. Nikol’skii and Ya. S. Bugrov, Elements of Linear Algebra and Analytical Geometry (Nauka, Moscow, 1980) (Translated into English, 1982; French, 1983; Spanish, 1984; Portuguese, 1986).
S. M. Nikol’skii and Ya. S. Bugrov, Differential and Integral Calculus (Nauka, Moscow, 1980) (Translated into English, 1982; French, 1983; Spanish, 1984; Portuguese, 1986).
S. M. Nikol’skii and P. I. Lizorkin, “Coercive Properties of Elliptic Equations: Variational Method,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 157, 90–118 (1981).
S. M. Nikol’skii and Ya. S. Bugrov, Differential Equations, Multiple Integrals, Series, and Functions of Complex Variable (Nauka, Moscow, 1981) (translated into English, 1983; French, 1983; Spanish, 1985; Portuguese, 1987).
S. M. Nikol’skii, Elements of Analysis (Nauka, Moscow, 1981) (translated into English, 1983; Spanish, 1984).
S. M. Nikol’skii and Ya. S. Bugrov, Problems Book (Nauka, Moscow, 1982) (translated into English, 1984; French, 1983; Spanish, 1987; Portuguese, 1988).
S. M. Nikol’skii and P. I. Lizorkin, “Coercive Properties of a Degenerate Elliptic Equation with Generalized Right-Hand Side,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 161, 157–183 (1983).
S. M. Nikol’skii and P. I. Lizorkin, “A Theorem Concerning Approximation on the Sphere,” Anal. Math. 9, 207–221 (1983).
S. M. Nikol’skii, “P. S. Aleksandrov and A. N. Kolmogorov in Dnepropetrovsk,” Usp. Mat. Nauk 38(4), 37–49 (1983).
S. M. Nikol’skii, Course of Mathematical Analysis, 3rd ed., updated (Nauka, Moscow, 1983), 2 vols. (translated into Italian, 1985).
S. M. Nikol’skii and P. I. Lizorkin, “Approximation by Spherical Polynomials,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 166, 185–200 (1984).
S. M. Nikol’skii and M. K. Potapov, Algebra: Textbook for Self-Education (Nauka, Moscow, 1985) (translated into English, 1987).
S. M. Nikol’skii and P. I. Lizorkin, “On the Theory of Approximations on the Sphere,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 172, 272–279 (1985).
S. M. Nikol’skii and P. I. Lizorkin, “Estimate for Derivatives of Harmonic Polynomials and Spherical Polynomials in L p,” Acta Sci. Math. (Szeged) 48, 401–416 (1985).
S. M. Nikol’skii and Ya. S. Bugrov, Differential Equations, Multiple Integrals, Series, and Functions of Complex Variable, 2nd ed. updated (Nauka, Moscow, 1985).
S. M. Nikol’skii and P. I. Lizorkin, “Approximation by Spherical Harmonics,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 173, 181–189 (1986).
S. M. Nikol’skii, “Approximation of Functions by Spherical Polynomials in the L p Metric”, Dokl. Akad. Nauk SSSR 289, 285–289 (1986).
S. M. Nikol’skii, M. K. Potapov, and N. N. Reshetnikov, Algebra: Trial Textbook for Grade 8 (Moscow, Prosveshchenie, 1986).
S. M. Nikol’skii and P. I. Lizorkin, “Approximation of Functions on the Sphere,” Izv. Akad. Nauk SSSR, Ser. Mat. 51, 635–651 (1987).
S. M. Nikol’skii and P. I. Lizorkin, “Functional Spaces on the Sphere Associated with Approximation Theory”, Mat. Zametki 41, 509–516 (1987).
S. M. Nikol’skii and P. I. Lizorkin, “New Approach to the Theory of Function Spaces B r p,ϑ on the Sphere,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 181, 213–221 (1988).
S. M. Nikol’skii, O. V. Besov, L. D. Kudryavtsev, and P. I. Lizorkin, “Studies in the Theory of Spaces of Differentiable Functions of Several Variables,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 182, 68–127 (1988).
S. M. Nikol’skii, P. I. Lizorkin, and N. V. Miroshin, “Weighted Function Spaces and Applications to Boundary Value Problems for Degenerate Elliptic Equations,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8, 4–30 (1988).
S. M. Nikol’skii and L. D. Kudryavtsev, “Spaces of Differentiable Functions of Several Variables and Embedding Theorems,” in Achievements in Science and Technology: Modern Problems in Mathematics: Fundamental Directions: Analysis (Moscow, VINITI, 1988), pp. 3–157 (translated into English, 1992).
S. M. Nikol’skii, M. K. Potapov, N. I. Reshetnikov, and A. V. Shevkin, Arithmetics: Textbook for Self-Education (Nauka, Moscow, 1988).
S. M. Nikol’skii and P. I. Lizorkin, “Approximation by Spherical Polynomials in L p (The Case of Symmetric Differences),” in Mathematical Modeling (Nauka, Moscow, 1989) pp. 227–237 (Modern Problems in Mathematics, Physics, and Computational Mathematics).
S. M. Nikol’skii and P. I. Lizorkin, “Functions Spaces of Mixed Smoothness from a Decomposition Point of View,” Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk SSSR 187, 143–161 (1989).
S. M. Nikol’skii, Elements of Analysis, 2nd ed., updated (Nauka, Moscow, 1989).
S. M. Nikol’skii, “Approximation by Functions of the Exponential Type and Polynomials on Manifolds,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 201, 273–301 (1991).
S. M. Nikol’skii, “On Approximation by Entire Functions of the Exponential Type and by Polynomials,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 204, 201–225 (1993).
S. M. Nikol’skii, “Approximation by Trigonometric Polynomials on Manifold,” Proceedings of International Symposium on Continuum Mechanics and Related Problems in Analysis, Tbilisi, 1991 (Metsniereba, Tbilisi, 1993), pp. 404–410.
S. M. Nikol’skii and P. I. Lizorkin, “Approximation of Functions on Manifold,” in Function Spaces, Differential Operators, and Nonlinear Analysis (Teubner, Stuttgart, 1993), pp. 185–199.
S. M. Nikol’skii, “In Memory of A.N. Kolmogorov,” in Kolmogorov in Memoirs (Nauka, Moscow, 1993), pp. 209–219 [in Russian].
S. M. Nikol’skii, “Approximation on Manifold by Algebraic Polynomials,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 210, 189–217 (1995).
S. M. Nikol’skii, “Approximation on Manifolds,” East J. Approx. 1(1), 1–24 (1995).
S. M. Nikol’skii, “Representation of Functions of Besov Class on Manifolds by Algebraic Polynomials,” Acta Math. Hung. 68(1–2), 99–109 (1995).
S. M. Nikol’skii, “A Certain Inequality for an Entire Function of Exponential Type”, J. Math. Sei. 80, 1597–1604 (1996).
S. M. Nikol’skii, “To the Theory of Implicit Functions,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 219, 258–268 (1997) [Proc. Steklov Math. Inst. 219, 254–264 (1997)].
S. M. Nikol’skii, Memoirs on Dnepropetrovsk (Dnepropetrovsk. Univ., Dnepropetrovsk, 1998).
S. M. Nikol’skii, “A Boundary Value Problem for Polynomials,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 227, 223–236 (1999) [Proc. Steklov Math. Inst. 227, 217–230 (1999)].
S. M. Nikol’skii, “More on a Boundary Value Problem with Polynomials,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 232, 286–288 (2001) [Proc. Steklov Math. Inst. 232, 278–280 (2001)].
S. M. Nikol’skii, “Besov Spaces,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 243, 9–12 (2003) [Proc. Steklov Math. Inst. 243, 3–6 (2003)].
S. M. Nikol’skii, “Liouville Classes of Harmonic Functions in the Circle,” “Approximation of Functions: Theoretical and Applied Aspects: Dedicated to the Memory of Professor A. I. Efimov” (MIET, Moscow, 2003), pp. 140–144 [in Russian].
S. M. Nikol’skii, Memoirs (Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk, Moscow, 2003)
S. M. Nikol’skii, My Mathematical Century (Fazis, Moscow, 2003).
S. M. Nikol’skii, “Compactness and Inequalities for Partial Derivatives,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 248, 194–203 (2005) [Proc. Steklov Math. Inst. 248, 187–196 (2005)].
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Original Russian Text © M.K. Kerimov, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 3, pp. 363–371.
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Kerimov, M.K. On the 100th birthday of Academician Sergei Mikhailovich Nikol’skii. Comput. Math. and Math. Phys. 46, 345–353 (2006). https://doi.org/10.1134/S0965542506030018
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DOI: https://doi.org/10.1134/S0965542506030018