Time-frequency analysis of localization operators

被引：196
|
作者：
Cordero, E
Gröchenig, K
机构：
[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
[2] Univ Turin, Dept Math, I-10124 Turin, Italy
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 205卷 / 01期
关键词：
localization operator; modulation space; Weyl calculus; convolution relations; Wigner distribution; short-time Fourier transform; Schatten class; Feichtinger's algebra;
D O I：
10.1016/S0022-1236(03)00166-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study a class of pseudodifferential operators known as time-frequency localization operators, Anti-Wick operators, Gabor-Toeplitz operators or wave packets. Given a symbol a and two windows phi(1), phi(2), we investigate the multilinear mapping from (a, phi(1), phi(2)) epsilon S'(R-2d) x S(R-d) x S(R-d) to the localization operator A(a)(phi1,phi2) and we give sufficient and necessary conditions for A(a)(phi1,phi2) to be bounded or to belong to a Schatten class. Our results are formulated in terms of time-frequency analysis, in particular we use modulation spaces as appropriate classes for symbols and windows. (C) 2003 Elsevier Inc. All rights reserved.
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页码：107 / 131
页数：25
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