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

Volume 55 / 1991

Zbigniew Pasternak-Winiarski Annales Polonici Mathematici 55 (1991), 287-300 DOI: 10.4064/ap-55-1-287-300

Abstract

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.

Authors

  • Zbigniew Pasternak-Winiarski

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