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Journal of the London Mathematical Society 2002 65(3):720-732; doi:10.1112/S0024610702003101
© 2002 by London Mathematical Society
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© The London Mathematical Society

Uniform Eigenvalue Estimates for Time-Frequency Localization Operators

F. De Mari, H. G. Feichtinger and K. Nowak

Dipartimento di Metodi e Modelli Matematici, Piazzale J. F. Kennedy Pad. D, 16129 Genova, Italy
Department of Mathematics, University of Vienna Strudlhofgasse 4, A-1090 Vienna, Austria
Department of Mathematics and Computer Science, Drexel University 3141 Chestnut Street, Philadelphia, PA 19104-2875, USA

Received 31 October 2000. Revision received 16 July 2001.

Time-variant filters based on Calderón and Gabor reproducing formulas are important tools in time-frequency analysis. The paper studies the behavior of the eigenvalues of these filters. Optimal two-sided estimates of the number of eigenvalues contained in the interval ({delta}1,{delta}2), where 0<{delta}1<{delta}2<1, are obtained. The estimates cover large classes of localization domains and generating functions.


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