Skip to main content
SpringerLink
Log in

K

  • Chapter
Encyclopaedia of Mathematics

Part of the book series: Encyclopaedia of Mathematics ((ENMA))

  • 1034 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antosik, P., and Swartz, C: Matrix methods in analysis, Vol. 1113 of Lecture Notes Math., Springer, 1985.

    MATH  Google Scholar 

  2. Klis, C: ‘An example of a non-complete (K) space’, Bull. Acad. Polon. Sci. 26 (1978), 415–420.

    MathSciNet  MATH  Google Scholar 

  3. Swartz, C: Infinite matrices and the gliding hump, World Sci., 1996.

    Book  MATH  Google Scholar 

  4. Besse, A.L.: Einstein manifolds, Springer, 1987.

    MATH  Google Scholar 

  5. Ochiai, T., et al.: Kähler metrics and moduli spaces, Vol. 18–11 of Adv. Stud. Pure Math., Kinokuniya, 1990.

    Google Scholar 

  6. Salamon, S.M.: ‘Quaternionic Kähler manifolds’, Invent. Math. 67 (1987), 175–203.

    MathSciNet  Google Scholar 

  7. Siu, Y.-T.: Lectures on Hermitian-Einstein metrics for stable bundles and Kahler-Einstein metrics, Birkhäuser, 1987.

    Google Scholar 

  8. Tian, G.: ‘Kähler-Einstein metrics on certain Kahler manifolds with C 1(M) > 0’, Invent. Math. 89 (1987), 225–246.

    Article  MathSciNet  MATH  Google Scholar 

  9. Tian, G., and Yau, S.-T.: ‘Kähler-Einstein metrics on complex surfaces with C 1 > 0’, Comm. Math. Phys. 112 (1987), 175–203.

    Article  MathSciNet  MATH  Google Scholar 

  10. Aubin, T.: Nonlinear analysis on manifolds, Springer, 1982.

    Book  MATH  Google Scholar 

  11. Besse, A.L.: Einstein manifolds, Springer, 1987.

    MATH  Google Scholar 

  12. Bourguignon, J.P., et al.: ‘Preuve de la conjecture de Calabi’, Astérisque 58 (1978).

    Google Scholar 

  13. Nadel, A.M.: ‘Multiplier ideal sheaves and existence of Kähler-Einstein metrics of positive scalar curvature’, Ann. of Math. 132 (1990), 549–596.

    Article  MathSciNet  MATH  Google Scholar 

  14. Ochiai, T., Et Al.: Kähler metrics and moduli spaces. Vol. 18–11 of Adv. Stud. Pure Math., Kinokuniya, 1990.

    Google Scholar 

  15. Siu, Y.-T.: Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics, Birkhäuser, 1987.

    MATH  Google Scholar 

  16. Tian, G.: ‘Kähler-Einstein metrics with positive scalar curvature’, Invent. Math. 137 (1997), 1–37.

    Article  Google Scholar 

  17. Yau, S.-T.: ‘On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation I’, Commun. Pure Appl. Math. 31 (1978), 339–411.

    Article  MATH  Google Scholar 

  18. Anstee, R.P., Przytycki, J.H., and Rolfsen, D.: ‘Knot polynomials and generalized mutation’, Topol. Appl. 32 (1989), 237–249.

    Article  MathSciNet  MATH  Google Scholar 

  19. Brandt, R.D., Lickorish, W.B.R., and Millett, K.C.: ‘A polynomial invariant for unoriented knots and links’, Invent. Math. 84 (1986), 563–573.

    Article  MathSciNet  MATH  Google Scholar 

  20. Garey, M.R., and Johnson, D.S.: Computers and intractability: A guide to theory of NP completeness, Freeman, 1979.

    MATH  Google Scholar 

  21. Ho, C.F.: ‘A new polynomial for knots and links; preliminary report’, Abstracts Amer. Math. Soc. 6, no. 4 (1985), 300.

    Google Scholar 

  22. Hoste, J., and Przytycki, J.H.: ‘A survey of skein modules of 3-manifolds’, in A. Kawauchi (ed.): Knots 90, Proc. Internat. Conf. Knot Theory and Related Topics, Osaka (Japan, August 15–19, 1990), W. de Gruyter, 1992, pp. 363–379.

    Google Scholar 

  23. Jaeger, F., Vertigan, D.L., and Welsh, D.J.A.: ‘On the computational complexity of the Jones and Tutte polynomials’, Math. Proc. Cambridge Philos. Soc. 108 (1990), 35–53.

    Article  MathSciNet  MATH  Google Scholar 

  24. Kauffman, L.H.: ‘An invariant of regular isotopy’, Trans. Amer. Math. Soc. 318, no. 2 (1990), 417–471.

    Article  MathSciNet  MATH  Google Scholar 

  25. Lickorish, W.B.R.: ‘Polynomials for links’, Bull. London Math. Soc. 20 (1988), 558–588.

    Article  MathSciNet  MATH  Google Scholar 

  26. Lickorish, W.B.R., and Millett, K.C.: ‘An evaluation of the F-polynomial of a link’: Differential topology: Proc. 2nd Topology Symp., Siegen/FRG 1987, Vol. 1350 of Lecture Notes Math., 1988, pp. 104–108.

    MathSciNet  Google Scholar 

  27. Przytycki, J.H.: ‘Equivalence of cables of mutants of knots’, Canad. J. Math. XLI, no. 2 (1989), 250–273.

    Article  MathSciNet  Google Scholar 

  28. Przytycki, J.H.: ‘Skein modules of 3-manifolds’, Bull. Acad. Polon. Math. 39, no. 1–2 (1991), 91–100.

    MathSciNet  MATH  Google Scholar 

  29. Thistlethwaite, M.B.: ‘On the Kauffman polynomial of an adequate link’, Invent. Math. 93 (1988), 285–296.

    Article  MathSciNet  MATH  Google Scholar 

  30. Turaev, V.G.: ‘The Conway and Kauffman modules of the solid torus’, J. Soviet Math. 52, no. 1 (1990), 2799–2805. (Zap. Nauchn. Sem. Lomi 167 (1988), 79–89.)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kawamata, Y.: ‘On the length of an extremal rational curve’, Invent. Math. 105 (1991), 609–611.

    Article  MathSciNet  MATH  Google Scholar 

  32. Kawamata, Y., Matsuda, K., and Matsuki, K.: ‘Introduction to the minimal model problem’: Algebraic Geometry (Sendai 1985), Vol. 10 of Adv. Stud. Pure Math., Kinokuniya&North-Holland, 1987, pp. 283–360.

    MathSciNet  Google Scholar 

  33. Beltrametti, M., and Sommese, A.J.: The adjunction theory of complex projective varieties, Vol. 16 of Experim. Math., W. de Gruyter, 1995.

    Book  MATH  Google Scholar 

  34. Bochner, S.: ‘Curvature and Betti numbers I–II’, Ann. of Math. 49/50 (1948/9), 379–390;

    Article  MathSciNet  Google Scholar 

  35. Bochner, S.: ‘Curvature and Betti numbers I–II’, Ann. of Math. 49/50 (1948/9), 77–93.

    Google Scholar 

  36. Castelnuovo, G., and Enriques, F.: ‘Sur quelques résultat nouveaux dans la théorie des surfaces algébriques’, in E. Picard and G. Simart (eds.): Théorie des Fonctions Algébriques, Vol. I–II.

    Google Scholar 

  37. Esnault, H., and Viehweg, E.: Lectures on vanishing theorems, Vol. 20 of DMV-Sem., Birkhäuser, 1992.

    Book  MATH  Google Scholar 

  38. Kawamata, Y.: ‘On the cohomology of Q-divisors’, Proc. Japan Acad. Ser. A 56 (1980), 34–35.

    Article  MathSciNet  MATH  Google Scholar 

  39. Kawamata, Y.: ‘A generalization of Kodaira-Ramanujam’s vanishing theorem’, Math. Ann. 261 (1982), 43–46.

    Article  MathSciNet  MATH  Google Scholar 

  40. Kawamata, Y., Matsuda, K., and Matsuki, K.: ‘Introduction to the minimal model problem’: Algebraic Geometry, Sendai 1985, Vol. 10 of Adv. Stud. Pure Math., 1987, pp. 283–360.

    MathSciNet  Google Scholar 

  41. Kleiman, S.L.: ‘The enumerative theory of singularities’, in P. Holme (ed.): Real and Complex Singularities, Oslo 1976, Sijthoff&Noordhoff, 1977, pp. 297–396.

    Chapter  Google Scholar 

  42. Kodaira, K.: ‘On a differential-geometric method in the theory of analytic stacks’, Proc. Nat. Acad. Sci. USA 39 (1953), 1268–1273.

    Article  MathSciNet  MATH  Google Scholar 

  43. Kollar, J.: ‘Higher direct images of dualizing sheaves I–II’, Ann. of Math. 123/4 (1986), 11–42; 171–202.

    Google Scholar 

  44. Miyaoka, Y.: ‘On the Mumford-Ramanujam vanishing theorem on a surface’: Journees de Geometrie Algebrique, Angers/France 1979, 1980, pp. 239–247.

    MathSciNet  Google Scholar 

  45. Picard, and Simart, G.: Théorie des fonctions algébriques I–II, Chelsea, reprint, 1971.

    Google Scholar 

  46. Ramanujam, C.P.: ‘Remarks on the Kodaira vanishing theorem’, J. Indian Math. Soc. 36 (1972), 41–51,

    MathSciNet  MATH  Google Scholar 

  47. Ramanujam, C.P.: ‘Remarks on the Kodaira vanishing theorem’ See also the Supplement: J. Indian Math. Soc. 38 (1974), 121–124.

    MathSciNet  MATH  Google Scholar 

  48. Roch, G.: ‘Über die Anzahl der willkürlichen Constanten in algebraischen Funktionen’, J. de Crelle 44 (1864), 207–218.

    Google Scholar 

  49. Shiffman, B., and Sommese, A.J.: Vanishing theorems on complex manifolds, Vol. 56 of Progr. Math., Birkhäuser, 1985.

    MATH  Google Scholar 

  50. Viehweg, E.: ‘Vanishing theorems’, J. Reine Angew. Math. 335 (1982), 1–8.

    MathSciNet  MATH  Google Scholar 

  51. Chavel, I.: Riemannian geometry: A modern introduction, Cambridge Univ. Press, 1995.

    MATH  Google Scholar 

  52. Kazdan, J.L.: ‘An inequality arising in geometry’, in A.I. Besse (ed.): Manifolds all of whose Geodesics are Closed, Springer, 1978, pp. 243–246; Appendix E.

    Google Scholar 

  53. Andersson, M., and Passare, M.: ‘Complex Kergin Interpolation’, J. Approx. Th. 64 (1991), 214–225.

    Article  MathSciNet  MATH  Google Scholar 

  54. Kergin, P.: ‘A natural interpolation of C K functions’, J. Approx. Th. 29 (1980), 278–293.

    Article  MathSciNet  MATH  Google Scholar 

  55. Micchelli, C.A., and Milman, P.: ‘A formula for Kergin interpolation in R k, J. Approx. Th. 29 (1980), 294–296.

    Article  MathSciNet  MATH  Google Scholar 

  56. Erdélyi, A., Magnus, W., and Oberhettinger, F.: Tables of integral transforms, McGraw-Hill, 1954, p. Chap. XII.

    Google Scholar 

  57. Kontorovich, M.I., and Lebedev, N.N.: ‘A method for the solution of problems in diffraction theory and related topics’, Zh. Eksper. Teor. Fiz. 8, no. 10–11 (1938), 1192–1206. (In Russian.)

    Google Scholar 

  58. Lebedev, N.N.: ‘Sur une formule d’inversion’, Dokl. Akad. Sci. USSR 52 (1946), 655–658.

    MATH  Google Scholar 

  59. Lebedev, N.N.: ‘Analog of the Parseval theorem for the one integral transform’, Dokl Akad. Nauk SSSR 68, no. 4 (1949), 653–656. (In Russian.)

    MATH  Google Scholar 

  60. Sneddon, I.N.: The use of integral transforms, McGraw-Hill, 1972, p. Chap. 6.

    MATH  Google Scholar 

  61. Vu Kim Tuan, and Yakubovich, S.B.: ‘The Kontorovich-Lebedev transform in a new class of functions’, Amer. Math. Soc. Transl. 137 (1987), 61–65.

    Google Scholar 

  62. Yakubovich, S.B.: Index transforms, World Sci., 1996, p. Chaps. 2;4.

    Book  MATH  Google Scholar 

  63. Yakubovich, S.B., and Fisher, B.: ‘On the Kontorovich- Lebedev transformation on distributions’, Proc. Amer. Math. Soc. 122, no. 3 (1994), 773–777.

    Article  MathSciNet  MATH  Google Scholar 

  64. Yakubovich, S.B., and Luchko, Yu.F.: The hypergeomet-ric approach to integral transforms and convolutions, Kluwer Acad. Publ., 1994.

    Book  Google Scholar 

  65. Zemanian, A.H.: ‘The Kontorovich-Lebedev transformation on distributions of compact support and its inversion’, Math. Proc. Cambridge Philos. Soc. 77 (1975), 139–143.

    Article  MathSciNet  MATH  Google Scholar 

  66. Arnol’d, V.I.: ‘Vassiliev’s theory of discriminants and knots’: First European Congress of Mathematicians (Paris), Birkhäuser, 1992, pp. 3–29.

    Google Scholar 

  67. Bar-Natan, D.: ‘On the Vassiliev knot invariants’, Topology 34 (1995), 423–472.

    Article  MathSciNet  MATH  Google Scholar 

  68. Bar-Natan, D., Garoufalidis, S., Rozansky, L., and Thurston, D.: ‘Wheels, wheeling, and the Kontsevich integral of the unknot’, preprint March (1997), q-alg/9703025.

    Google Scholar 

  69. Chmutov, S.V., and Duzhin, S.V.: ‘The Kontsevich integral’, Acta Applic. Math, (to appear), available via anonymous ftp: pier.botik.ru, file: pub/local/zmr/ki.ps.gz.

    Google Scholar 

  70. Kontsevich, M.: ‘Vassiliev’s knot invariants’, Adv. Soviet Math. 16 (1993), 137–150.

    MathSciNet  Google Scholar 

  71. Le, T.Q.T., and Murakami, J.: ‘The universal Vassiliev-Kontsevich invariant for framed oriented links’, Compositio Math. 102 (1996), 42–64.

    MathSciNet  Google Scholar 

  72. Vassiliev, V.A.: ‘Theory of singularities and its applications’, in V.I. Arnol’d (ed.): Advances in Soviet Math., Vol. 1, Amer. Math. Soc, 1990, pp. 23 – 69.

    Google Scholar 

  73. Ablowitz, M.J., and Clarkson, P.A.: Solitons, nonlinear evolution equations and inverse scattering, Cambridge Univ. Press, 1991.

    Book  MATH  Google Scholar 

  74. Beals, R., Deift, P., and Tomei, C.: Direct and inverse scattering on the line, Amer. Math. Soc., 1988.

    MATH  Google Scholar 

  75. Date, E., Kashiwara, M., Jimbo, M., and Miwa, T.: ‘Transformation groups for soliton equation’: Nonlinear Integrate Systems — Classical Theory and Quantum Theory Proc. RIMS Symp., Kyoto 1981, 1983, pp. 39–119.

    MathSciNet  Google Scholar 

  76. Kadomtsev, B.B., and Petviashvili, V.J.: ‘On the stability of solitary waves in weakly dispersive media’, Soviet Phys. Dokl. 15 (1970), 539–541.

    MATH  Google Scholar 

  77. Krichever, I.M.: ‘Methods of algebraic geometry in the theory of non-linear equations’, Russian Math. Surveys 32, no. 6 (1977), 185–213.

    Article  MATH  Google Scholar 

  78. Krichever, I.M., and Novikov, S.P.: ‘Holomorphic bundles over algebraic curves and nonlinear equations’, Russian Math. Surveys 35, no. 6 (1980), 53–79. (Uspekhi Mat. Nauk 35, no. 6 (216) (1980), 47–68.)

    Article  MathSciNet  MATH  Google Scholar 

  79. Mulase, M.: ‘Algebraic theory of the KP equations’, in R. Penner et al. (eds.): Perspectives in Mathematical Physics. Proc. Conf. Interface Math. And Physics, Taiwan summer 1992, Vol. 3 of Conf. Proc. Math. Phys., Internat. ress, 1994, pp. 151–217, Also: Special Session On Topics In Geometry And Physics, Los Angeles, Winter 1992.

    Google Scholar 

  80. Nakayashiki, A.: ‘Structure of Baker-Akhiezer modules of principally polarized abelian varieties, commuting partial differential operators and associated integrable systems’, Duke Math. J. 62, no. 2 (1991), 315–358.

    Article  MathSciNet  MATH  Google Scholar 

  81. Natanzon, S.M.: ‘Real nonsingular finite zone solutions of soliton equations’, in S.P. Novikov (ed.): Topics in Topol. Math. Physics, Vol. 170 of Transi. Ser. 2, Amer. Math. Soc., 1995, pp. 153–183.

    Google Scholar 

  82. Sato, M.: ‘The KP hierarchy and infinite-dimensional Grassmann manifolds’: Theta functions. Proc. 35th Summer Res. Inst. Bowdoin Coll., Brunswick/ME 1987, Vol. 49:1 of Proc. Symp. Pure Math., Amer. Math. Soc., 1989, pp. 51–66.

    Google Scholar 

  83. Shiota, T.: ‘Characterization of Jacobian varieties in terms of soliton equations’, Invent. Math. 83 (1986), 333–382.

    Article  MathSciNet  MATH  Google Scholar 

  84. Witten, E.: ‘Two-dimensional gravity and intersection theory on moduli space’, J. Diff. Geom. Suppl. 1 (1991), 243–310.

    Google Scholar 

  85. Akhiezer, N.I.: The classical moment problem, Hafner, 1965. (Translated from the Russian.)

    MATH  Google Scholar 

  86. Berg, C.: ‘The cube of a normal distribution is indeterminate’, Ann. of Probab. 16 (1988), 910–913.

    Article  MATH  Google Scholar 

  87. Berg, C.: ‘Indeterminate moment problems and the theory of entire functions’, J. Comput. Appl. Math. 65 (1995), 27–55.

    Article  MathSciNet  MATH  Google Scholar 

  88. Heyde, C.C.: ‘On a property of the lognormal distribution’, J. R. Statist. Soc. Ser. B 29 (1963), 392–393.

    MathSciNet  Google Scholar 

  89. Krein, M.G.: ‘On one extrapolation problem of A.N. Kolmogorov’, Dokl. Akad. Nauk SSSR 46, no. 8 (1944), 339–342. (In Russian.)

    Google Scholar 

  90. Lin, G.D.: ‘On the moment problem’, Statist. Probab. Lett. 35 (1997), 85–90.

    Article  MathSciNet  MATH  Google Scholar 

  91. Pedersen, H.L.: ‘On Krein’s theorem for indeterminacy of the classical moment problem’, J. Approx. Th. 95 (1998), 90–100.

    Article  MATH  Google Scholar 

  92. Prohorov, Yu.V., and Rozanov, Yu.A.: Probability theory, Springer, 1969. (Translated from the Russian.)

    Google Scholar 

  93. Simon, B.: ‘The classical moment problem as a self-adjoint finite difference operator’, Adv. Math. 137 (1998), 82–203.

    Article  MathSciNet  MATH  Google Scholar 

  94. Slud, E.V.: ‘The moment problem for polynomial forms of normal random variables’, Ann. of Probab. 21 (1993), 2200–2214.

    Article  MathSciNet  MATH  Google Scholar 

  95. Stoyanov, J.: Counterexamples in probability, 2nd ed., Wiley, 1997.

    MATH  Google Scholar 

  96. Stoyanov, J.: ‘Krein condition in probabilistic moment problems’, Bernoulli to appear (1999/2000).

    Google Scholar 

  97. Davis, P.J., and Rabinowitz, P.: Methods of numerical integration, second ed., Acad. Press, 1984.

    MATH  Google Scholar 

  98. Patterson, T.N.L.: ‘The optimum addition of points to quadrature formulae’, Math. Comput. 22 (1968), 847–856.

    Article  MATH  Google Scholar 

  99. Peherstorfer, F.: ‘Weight functions admitting repeated positive Kronrod quadrature’, BIT 30 (1990), 241–251.

    Article  MathSciNet  Google Scholar 

  100. Piessens, R., et al.: QUADPACK: a subroutine package in automatic integration, Springer, 1983.

    MATH  Google Scholar 

  101. Rabinowitz, P., Elhay, S., and Kautsky, J.: ‘Empirical mathematics: the first Patterson extension of Gauss-Kronrod rules’, Internat. J. Computer Math. 36 (1990), 119–129.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CWI, P.O.Box 94079, 1090GB, Amsterdam, The Netherlands

    Prof. Dr. Michiel Hazewinkel

Authors
  1. Prof. Dr. Michiel Hazewinkel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CWI, P.O.Box 94079, 1090GB, Amsterdam, The Netherlands

    Michiel Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Kluwer Academic Publishers and Elliott H. Lieb for “Lieb-Thirring inequalities” and “Thomas-Fermi theory”

About this chapter

Cite this chapter

Hazewinkel, M. (2000). K. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1279-4_11

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-1279-4_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5378-7

  • Online ISBN: 978-94-015-1279-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation