Short-Time Fourier Transform Analysis of Localization Operators

We perform a detailed study of the boundedness properties for localization operators. The language and the tools employed are provided by time-frequency analysis. In particular, the time-frequency representation named short-time Fourier Transform (STFT) is used to both define and get the boundedness properties of localization operators. Our results widen most of the literature on the topic. Moreover, the sufficient conditions are worked out by STFT estimates rather than Weyl connections. Besides, the necessary boundedness conditions are referred to a fixed pair of window functions, so that we can claim the optimality of our results. Finally, in a different direction, we shall deal with the problem of finding symbol conditions for Weyl operators that guarantee to rewrite them as Wick operators.