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Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

Published 30 Aug 2022 in math.CV | (2208.14291v2)

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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