Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

2022/08/30 by Boudreaux, Blake J.
#Complex Variables (math.CV) #FOS: Mathematics #Primary 32A25 #Secondary 32A36

paper · doi:10.48550/arxiv.2208.14291

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.

Related

• The Bergman Kernel on some Hartogs domains
• An application of a Diederich-Ohsawa theorem in characterizing some Hartogs domains
• Some Topics Related to Bergman Kernel
• Reproducing kernels of some weighted Bergman spaces
• The Bergman kernel of a certain Hartogs domain and the polylogarithm function