Symbolic calculus and Fredholm property for localization operators
Functional Analysis
2011-04-27 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.math/0509153,
title = {Symbolic calculus and Fredholm property for localization operators},
author = {Elena Cordero and Karlheinz Gröchenig},
journal= {arXiv preprint arXiv:math/0509153},
year = {2011}
}