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arXiv · 2208.14291

Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

Blake J. Boudreaux
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Abstract

We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergman kernel of a Hartogs domain as a series involving weighted Bergman kernels over its base, as well as a "transformation" formula for some weighted Bergman kernels. Other relationships of this type are presented.

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Blake J. Boudreaux. 2022-08-30. Relationships Between the Bergman Kernels of Hartogs Domains and Their Base. https://arxiv.org/abs/2208.14291

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