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1991 | 55 | 1 | 287-300
Tytuł artykułu

On the dependence of the Bergman function on deformations of the Hartogs domain

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We apply the Rudin idea to represent the Bergman kernel of the Hartogs domain as the sum of a series of weighted Bergman functions in the study of the dependence of this kernel on deformations of the domain. We prove that the Bergman function depends smoothly on the function defining the Hartogs domain.
Słowa kluczowe
Rocznik
Tom
55
Numer
1
Strony
287-300
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-09-14
Twórcy
  • Institute of Mathematics, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warszawa, Poland
Bibliografia
  • [1] J. Burbea and P. Masani, Banach and Hilbert Spaces of Vector-Valued Functions, Res. Notes Math. 90, Pitman, Boston 1984.
  • [2] F. Forelli and W. Rudin, Projections on spaces of holomorphic functions in balls, Indiana Univ. Math. J. 24 (1974), 593-602.
  • [3] R. E. Greene and S. G. Krantz, Stability of the Bergman kernel and curvature properties of bounded domains, in: Recent Developments in Several Complex Variables, J. Fornaess (ed.), Ann. of Math. Stud. 100, Princeton Univ. Press, Princeton, N.J., 1981.
  • [4] R. E. Greene and S. G. Krantz, Deformation of complex structures, estimates for the ∂̅ equation, and stability of the Bergman kernel, Adv. in Math. 43 (1982), 1-86.
  • [5] S. G. Krantz, Function Theory of Several Complex Variables, Interscience-Wiley, New York 1982.
  • [6] E. Ligocka, The regularity of the weighted Bergman projection, in: Seminar of Deformation Theory 1982/84, Lecture Notes in Math. 1165, Springer, 1985, 197-203.
  • [7] E. Ligocka, On the Forelli-Rudin construction and weighted Bergman projections, Studia Math. 94 (1989), 257-272.
  • [8] K. Maurin, Analysis, Part 1, Elements, PWN-Reidel, Warszawa-Dordrecht 1976.
  • [9] K. Maurin, Analysis, Part 2, Integration, Distributions, Holomorphic Functions, Tensor and Harmonic Analysis, PWN-Reidel, Warszawa-Dordrecht 1980.
  • [10] T. Mazur, On the complex manifolds of Bergman type, to appear.
  • [11] Z. Pasternak-Winiarski, On the dependence of the reproducing kernel on the weight of integration, J. Funct. Anal. 94 (1990), 110-134.
  • [12] Z. Pasternak-Winiarski, On weights which admit the reproducing kernel of Bergman type, Internat. J. Math. and Math. Sci., to appear.
  • [13] W. Rudin, Function Theory in the Unit Ball in $ℂ^n$, Springer, Berlin 1980.
  • [14] B. V. Shabat, Introduction to Complex Analysis, 3rd ed., Nauka, Moscow 1985 (in Russian).
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv55z1p287bwm
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