A Szegő-type theorem for Gabor-Toeplitz localization operators

Abstract

. Our main result is a Szego type theorem for time-frequency localization operators based on the Gabor reproducing formula. As corollaries we deduce statements about the asymptotic behavior of the distribution of the eigenvalues and the size of the plunge region. The asymptotic limit which we consider corresponds to expanding symbols by dilations and increasing the dilation factor to innity. The symbols are assumed to be non-negative, bounded and integrable. 1. Introduction and Preliminaries Linear time-frequency methods such as Gabor expansions or the short time Fourier transform provide ways of analyzing signals by describing their frequency content as it varies over time. In contrast to quadratic methods Gabor expansions allow to manipulate signals in a linear way. The resulting time-variant ltering procedures allow to isolate partial signals or suppress the noise. Gabor expansions have a long history. They have been applied by engineers for decades. Despite this fact thei...