Traces of functions in Fock spaces on lattices of critical density

TL;DR

This paper characterizes the values of functions in Fock spaces on critical density lattices using size and cancellation conditions involving discrete transforms, advancing understanding of function behavior in complex analysis.

Contribution

It introduces a novel description of Fock space functions on critical density lattices through discrete transforms and cancellation conditions, extending Levin's scheme.

Findings

Characterization of Fock space functions on critical density lattices

Use of discrete Cauchy and Beurling-Ahlfors transforms

Conditions involving size and cancellation for function values

Abstract

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.