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