Zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain and the interlacing property

TL;DR

This paper investigates the zeros of the Bergman kernel in the Fock-Bargmann-Hartogs domain, revealing how their existence depends on the domain's parameters through an interlacing property.

Contribution

It introduces a novel analysis of the zero distribution of the Bergman kernel in relation to domain parameters using interlacing properties.

Findings

Zeros depend on parameters m and n

Interlacing property characterizes zero existence

Provides conditions for zero-free regions

Abstract

In this paper we consider the zeros of the Bergman kernel of the Fock-Bargmann-Hartogs domain $D_{n,m}$. We describe how the existence of zeros of the Bergman kernel depends on the integers $m$ and $n$ with the help of the interlacing property.