Reproducing kernels of some weighted Bergman spaces

TL;DR

This paper extends the theory of Bergman kernels to weighted spaces, providing a general formula for the reproducing kernel that enables explicit calculations for various weights and domains.

Contribution

It introduces a general form of the weighted Bergman reproducing kernel, facilitating explicit computations for specific weights and domains.

Findings

Derived a general formula for weighted Bergman kernels

Enabled explicit calculations for specific weights and domains

Extended classical Bergman kernel theory to weighted cases

Abstract

Herein, the theory of Bergman kernel is developed to the weighted case. A general form of weighted Bergman reproducing kernel is obtained, by which we can calculate concrete Bergman kernel functions for specific weights and domains.