Curious properties of canonical divisors in weighted Bergman spaces

TL;DR

This paper investigates the properties of weighted Bergman kernels on the unit disk, focusing on subspace kernels and their division properties, revealing new insights into their structure and behavior.

Contribution

It introduces a simple formula for the reproducing kernel of subspaces of weighted Bergman spaces and studies their division properties, advancing understanding of these kernels.

Findings

Derived a simple formula for subspace kernels from weighted Bergman kernels

Analyzed division properties of the new kernels

Enhanced understanding of kernel structure in weighted Bergman spaces

Abstract

We study properties of the weighted Bergman hernel on the unit disk. As we restrict to the subspace of all functions that vanish at a given point, we obtain the reproducing kernel for the subspace from the above weighted Bergman kernel via a simple formula. Division properties of this new kernel are studied.