Cohen class of time-frequency representations and operators: boundedness and uncertainty principles

TL;DR

This paper investigates the boundedness and uncertainty principles of Cohen class time-frequency representations and associated operators, extending classical results to more general operators in the $L^p$ setting.

Contribution

It introduces a boundedness result and an uncertainty principle for a broad class of Cohen type operators, generalizing previous localization operator results.

Findings

Proves an uncertainty principle involving $oldsymbol{ ext{ε}}$-concentration.

Establishes boundedness of Cohen class operators in $L^p$ spaces.

Extends classical localization operator results to more general Cohen class operators.

Abstract

This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered. For these operators, which include all usual quantizations, we prove a boundedness result in the $L^p$ functional setting and a form of uncertainty principle analogous to that for localization operators.