Decay and smoothness for eigenfunctions of localization operators

[摘要] We study decay and smoothness properties for eigenfunctions of compact localization operators A(a)(phi 1,phi 2). Operators A(a)(phi 1,phi 2) with symbols a in the wide modulation space M-p,M-infinity (containing the Lebesgue space L-p), p0 (subspaces of M-p,M-infinity(R(2)d), p>2d/s) the L-2-eigenfunctions of A(a)(phi 1,phi 2) 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. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-15

[关键词] Time-frequency analysis;Localization operators;Short-time Fourier transform;Quasi-Banach spaces;Modulation spaces;Wiener amalgam spaces