Finite Rank Bargmann-Toeplitz Operators with Non-Compactly Supported Symbols

TL;DR

This paper extends the characterization of finite rank Toeplitz operators in Fock spaces to symbols with rapid decay at infinity, removing the previous compact support restriction using a new approximation theorem.

Contribution

It introduces a novel approach to characterize finite rank Toeplitz operators with non-compactly supported symbols in Fock spaces.

Findings

Characterization applies to symbols with rapid decay, not just compact support

New version of Stone-Weierstrass approximation theorem developed

Extends previous results to broader class of symbols

Abstract

Theorems about characterization of finite rank Toeplitz operators in Fock-Segal-Bargmann spaces, known previously only for symbols with compact support, are carried over to symbols without that restriction, however with a rather rapid decay at infinity. The proof is based upon a new version of the Stone-Weierstrass approximation theorem.