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UNIFORM EIGENVALUE ESTIMATES FOR TIME-FREQUENCY LOCALIZATION OPERATORS

Published online by Cambridge University Press:  24 March 2003

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

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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 720 - 732
Copyright
The London Mathematical Society, 2002

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