A Tale of Three Kernels

TL;DR

This paper explores the properties and relationships of the Bergman, Szeg\

Contribution

It provides new insights into the connections between these three fundamental kernels in complex analysis.

Findings

Established relationships between the kernels.

Provided expository explanations of kernel properties.

Identified new properties and connections.

Abstract

We consider the Bergman, Szeg\H{o}, and Poisson Szeg\H{o} kernels on a domain in $\CC$ or $\CC^n$. Various properties and relationships are established. The paper has both an expository component and a research component.