Norm bounds for self-adjoint Toeplitz operators with non-radial symbols on the Fock space

TL;DR

This paper extends existing norm bounds for self-adjoint Toeplitz operators on the Fock space to include non-radial, bounded, and integrable symbols, using isoperimetric inequalities and advanced approximation techniques.

Contribution

It introduces a novel approach to bounding norms of non-radial symbols in Fock-Toeplitz operators, expanding the scope of previous results.

Findings

Norm bounds established for non-radial symbols

Application of Nicola-Tilli isoperimetric inequality in Fock space

Extension of Galbis' methods to two-dimensional setting

Abstract

In this paper we extend Galbis' elegant norm bounds for self-adjoint Toeplitz operators on the Fock space to bounded and integrable symbols which are non-radial. The main ingredients are a transplantation of the remarkable Nicola-Tilli isoperimetric inequality to the realm of Fock-Toeplitz operator theory and a two-dimensional adaption of Galbis' integration and approximation arguments.