Journal of Fourier Analysis and Applications

, Volume 12, Issue 4, pp 371–392

Symbolic Calculus and Fredholm Property for Localization Operators

Article

DOI: 10.1007/s00041-005-5077-7

Cite this article as:
Cordero, E. & Grochenig, K. J Fourier Anal Appl (2006) 12: 371. doi:10.1007/s00041-005-5077-7

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.

Copyright information

© Birkhauser Boston 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of TorinoTorinoItaly
  2. 2.Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090WienAustria