Symbolic calculus and Fredholm property for localization operators

Details Symbolic calculus and Fredholm property for localization operators Symbolic calculus and Fredholm property for localization operators

2005-09-07

arxiv.org/abs/math/0509153v1

J.~Fourier Anal.~Appl.~12(3) (2006), 371-392

Mathematics

Functional Analysis

Scientific paper

We study the composition of time-ffrequency localization operators (wavepacket operators) and develop a symbolic calculus of such operators on modulation spaces. The use of time-frequency methods (phase space methods) allows the use of rough symbols of ultra-rapid growth in place of smooth symbols in the standard classes. As the main application it is shown that, in general, a localization operators possesses the Fredholm property, and thus its range is closed in the target space.

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