Uniform Eigenvalue Estimates for Time‐Frequency Localization Operators

Source 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 (δ 1 ,δ 2 ), where 0<δ 1 <δ 2 <1, are obtained. The estimates cover large classes of localization domains and generating functions.