DeMari, Fillipo;Feichtinger, Hans G.;Nowak, Krzysztof

Uniform eigenvalue estimates for time-frequency localization operators

J. London Math. Soc. Vol.65 No.3 (2002) p.720-732, Zbl:1033.47021, MR1895743

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abstract

Time-variant filters based on Calderon and Gabor reproducing formulas are important tools in time-frequency analysis. The paper studies the behaviour of the eigenvalues of these filters. Optimal two-sided estimates of the number of eigenvalues contained in the intervall (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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