Berezin transform in polynomial Bergman spaces

TL;DR

This paper investigates the Berezin transform within weighted polynomial Bergman spaces, focusing on the properties of the reproducing kernel and potential applications to random matrix theory.

Contribution

It provides new insights into the Berezin transform and reproducing kernels in polynomial Bergman spaces, with implications for random matrix theory.

Findings

Analysis of the reproducing kernel for weighted polynomial Bergman spaces

Results on the Berezin transform in these spaces

Potential applications to random matrix theory

Abstract

We study the reproducing kernel for weighted polynomial Bergman spaces and consider applications to the Berezin transform. Some of our results have applications in random matrix theory, a topic which we discuss in a separate (companion) paper.