Time-variant filters based on Caldero ́n 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 (δ1,δ2), where 0 < δ1 < δ2 < 1, are obtained. The estimates cover large classes of localization domains and generating functions.
Uniform eigenvalue estimates for time-frequency localization operators
DE MARI CASARETO DAL VERME, FILIPPO;
2002-01-01
Abstract
Time-variant filters based on Caldero ́n 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 (δ1,δ2), where 0 < δ1 < δ2 < 1, are obtained. The estimates cover large classes of localization domains and generating functions.
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