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

Abstract

This paper presents a proof of an uncertainty principle of Donoho–Stark type involving ε-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 Lp functional setting and a form of uncertainty principle analogous to that for localization operators.