Toeplitz operators associated with the directional short-time Fourier transform and applications

Abstract

In the present article, we prove a Shapiro uncertainty principle for the directional short-time Fourier transform. Next, we introduce the notion of Toeplitz operators associated with the directional short-time Fourier transform. Particularly, we study the trace class properties of such operators and prove that they belong to the Schatten–von Neumann class. Next, we investigate the boundedness and compactness of these Toeplitz operators in the \(L^{p}\)-spaces. Finally, we introduce and study the generalized spectrogram associated with these Toeplitz operators.