Zero and uniqueness sets for Fock spaces

TL;DR

This paper characterizes zero sets in Fock spaces that maintain their zero set property under subsets and investigates the stability of certain uniqueness sets with zero excess.

Contribution

It provides a characterization of zero sets in Fock spaces that are stable under subset formation and studies the stability of specific uniqueness sets with zero excess.

Findings

Identifies conditions for zero sets to remain zero sets under subsets

Analyzes stability of uniqueness sets with zero excess

Contributes to understanding of zero and uniqueness sets in Fock spaces

Abstract

We characterize zero sets for which every subset remains a zero set too in the Fock space $\mathcal{F}^p$, $1\leq p<\infty$. We are also interested in the study of a stability problem for some examples of uniqueness set with zero excess in Fock spaces.