Archivio Istituzionale della RicercaWe present localization operators via the short-time Fourier transform. For both modulation and ultra-modulation spaces framework, well-known results about boundedness and Schatten-von Neumann class are reported. Asymptotic eigenvalues’ distribution and decay and smoothness properties for L2-eigenfunctions are exhibited. Eventually, we make a conjecture about smoothness of L2-eigenfunctions for localization operators with Gelfand–Shilov windows and symbols in ultra-modulation spaces.
Time–frequency localization operators: State of the art / Bastianoni, F. (APPLIED AND NUMERICAL HARMONIC ANALYSIS). - In: Landscapes of time-frequency analysis[s.l] : Birkhauser, 2020. - ISBN 9783030560041. - pp. 63-74 [10.1007/978-3-030-56005-8_4]
Time–frequency localization operators: State of the art
Bastianoni F.
2020
Abstract
We present localization operators via the short-time Fourier transform. For both modulation and ultra-modulation spaces framework, well-known results about boundedness and Schatten-von Neumann class are reported. Asymptotic eigenvalues’ distribution and decay and smoothness properties for L2-eigenfunctions are exhibited. Eventually, we make a conjecture about smoothness of L2-eigenfunctions for localization operators with Gelfand–Shilov windows and symbols in ultra-modulation spaces.
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https://hdl.handle.net/11583/2950754