On the boundedness of certain operators of convolution type on Fock spaces

TL;DR

This paper establishes precise conditions under which convolution-type operators are bounded on twisted Fock spaces, advancing understanding of operator behavior in complex functional analysis.

Contribution

It provides necessary and sufficient criteria for the boundedness of convolution operators on twisted Fock spaces, a novel characterization in this context.

Findings

Derived explicit conditions for boundedness of convolution operators.

Extended the theory of operators on Fock spaces to twisted variants.

Identified key properties of convolution kernels affecting boundedness.

Abstract

We find necessary and sufficient conditions on the convolution kernels $ \varphi $ so that certain operators on twisted Fock spaces $\mathcal{F}^\lambda(\C^{2n})$ are bounded.