Time-frequency localization for the short time Fourier transform

摘要

We use some estimating of orthogonal projection in a reproducing kernel Hilbert space, to prove a sharp quantitaive form of Shapiro's mean dispersion theroem with generalized dispersion for the short time Fourier transform. Other forms of localization of orthonormal sequences in L-2d) notably the umbrella theorem, are also proved for the short time Fourier transform.