Time-Frequency Localization Operators and a Berezin Transform

Karlheinz Gröchenig, Dominik Bayer

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed


Time–frequency localization operators are a quantization procedure that maps symbols on R 2d 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 L 2(R d). 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.

Seiten (von - bis)95-117
FachzeitschriftIntegral Equations and Operator Theory
PublikationsstatusVeröffentlicht - 1 Mai 2015

ÖFOS 2012

  • 101002 Analysis