Time-Frequency Localization Operators and a Berezin Transform

Time-frequency localization operators are a quantization procedure that maps symbols on to operators and depends on two window functions. We study the range of this quantization and its dependence on the window functions. If the If the short-time Fourier transform of the windows does not have any zero, then the range is dense in the Schatten p-classes. The main tool is new version of the Berezin transform associated to operators on . Although some results are analogous to results about Toeplitz operators on spaces of holomorphic functions, the absence of a complex structure requires the development of new methods that are based on time-frequency analysis.