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. Our main result is a Szego type theorem for time-frequency localizationoperators based on the Gabor reproducing formula. As corollaries we deduce statementsabout the asymptotic behavior of the distribution of the eigenvalues and thesize of the plunge region. The asymptotic limit which we consider corresponds toexpanding symbols by dilations and increasing the dilation factor to innity. Thesymbols are assumed to be non-negative, bounded and integrable.1. Introduction and...

A Szegő-type theorem for Gabor-Toeplitz localization operators