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Symbolic Calculus and Fredholm Property for Localization Operators

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Abstract

We study the composition of time-frequency 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 operator possesses the Fredholm property, and thus its range is closed in the target space.

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Authors and Affiliations

  1. Department of Mathematics, University of Torino, Torino, Italy

    Elena Cordero

  2. Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090, Wien, Austria

    Karlheinz Grochenig

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  1. Elena Cordero
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  2. Karlheinz Grochenig
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Correspondence to Elena Cordero or Karlheinz Grochenig.

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Cordero, E., Grochenig, K. Symbolic Calculus and Fredholm Property for Localization Operators. J Fourier Anal Appl 12, 371–392 (2006). https://doi.org/10.1007/s00041-005-5077-7

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  • DOI: https://doi.org/10.1007/s00041-005-5077-7

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