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Symbolic calculus and Fredholm property for localization operators

Elena Cordero·Karlheinz Gröchenig
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Abstract

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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Elena Cordero, Karlheinz Gröchenig. 2005-09-07. Symbolic calculus and Fredholm property for localization operators. https://arxiv.org/abs/math/0509153

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