We study decay and smoothness properties for eigenfunctions of compact localization operators. Operators with symbols a in the wide modulation space M^{p,∞} (containing the Lebesgue space Lp), p<∞, and windows φ_1,φ_2 in the Schwartz class S are known to be compact. We show that their L^2-eigenfuctions with non-zero eigenvalues are indeed highly compressed onto a few Gabor atoms. Similarly, for symbols a in the weighted modulation spaces , the L^2-eigenfunctions of localization operators are actually Schwartz functions. An important role is played by quasi-Banach Wiener amalgam and modulation spaces. As a tool, new convolution relations for modulation spaces and multiplication relations for Wiener amalgam spaces in the quasi-Banach setting are exhibited.

Decay and smoothness for eigenfunctions of localization operators

Bastianoni F.;Cordero E.;
2020-01-01

Abstract

We study decay and smoothness properties for eigenfunctions of compact localization operators. Operators with symbols a in the wide modulation space M^{p,∞} (containing the Lebesgue space Lp), p<∞, and windows φ_1,φ_2 in the Schwartz class S are known to be compact. We show that their L^2-eigenfuctions with non-zero eigenvalues are indeed highly compressed onto a few Gabor atoms. Similarly, for symbols a in the weighted modulation spaces , the L^2-eigenfunctions of localization operators are actually Schwartz functions. An important role is played by quasi-Banach Wiener amalgam and modulation spaces. As a tool, new convolution relations for modulation spaces and multiplication relations for Wiener amalgam spaces in the quasi-Banach setting are exhibited.
2020
492
2
1
19
https://arxiv.org/abs/1902.03413
Localization operators; Modulation spaces; Quasi-Banach spaces; Short-time Fourier transform; Time-frequency analysis; Wiener amalgam spaces
Bastianoni F.; Cordero E.; Nicola F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1782114
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