The Weighted Bergman Kernel and the Green's Function

TL;DR

This paper explores the relationship between the weighted Bergman kernel and Green's function on complex domains, providing insights into their interconnected properties and potential applications in complex analysis.

Contribution

It establishes a new connection between weighted Bergman kernels and Green's functions on complex domains, enhancing understanding of their interplay.

Findings

Derived formulas linking Bergman kernel and Green's function

Extended classical results to weighted settings

Provided new tools for analysis on complex domains

Abstract

We study the connection between weighted Bergman kernel and Green's function on a domain W lying in C for which the Green's function exists.