The Lee-Yang and P\'olya-Schur programs. III. Zero-preservers on Bargmann-Fock spaces

TL;DR

This paper characterizes linear operators that preserve zero-restrictions on entire functions within weighted Bargmann-Fock spaces, extending prior results and providing an optimal formal Lee-Yang theorem.

Contribution

It extends previous zero-preservation characterizations to entire functions in Bargmann-Fock spaces, offering a new optimal formal Lee-Yang theorem.

Findings

Characterization of zero-preserving operators on entire functions

Extension of Borcea and author's previous results

An optimal formal Lee-Yang theorem

Abstract

We characterize linear operators preserving zero-restrictions on entire functions in weighted Bargmann-Fock spaces. The characterization extends previous results of J. Borcea and the author to the realm of entire functions, and translates into an optimal, albeit formal, Lee-Yang theorem.