Time-frequency analysis on modulation spaces Mmp,q, 0 < p,q ≤ ∞

被引：64
|
作者：
Galperin, YV [1 ]
Samarah, S
机构：
[1] E Stroudsburg Univ Penn, Dept Math, E Stroudsburg, PA USA
[2] Jordan Univ Sci & Technol, Dept Math & Stat, Irbid, Jordan
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2004年 / 16卷 / 01期
关键词：
modulation space; short-time Fourier transform; Gabor expansion; function spaces;
D O I：
10.1016/j.acha.2003.09.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The theory of modulation spaces M-m(p.q) is extended to the general case 0 < p, q less than or equal to infinity. It is shown that these spaces admit an atomic decomposition and are characterized by decay and summability properties of Gabor coefficients. A large space of admissible windows is constructed which contains the Schwartz class in the case of weights of polynomial growth and has the form of a union of modulation spaces. It is shown that different windows in this space yield equivalent modulation space quasi-norms. (C) 2003 Elsevier Inc. All rights reserved.
引用
收藏
页码：1 / 18
页数：18
相关论文
共 50 条
  • [1] Time frequency analysis and multipliers of the spaces M(p, q) (Rd) and S(p, q) (Rd)
    Gurkanli, A. Turan
    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 2006, 46 (03): : 595 - 616
  • [2] Sharp estimates of the embedding constants for Besov spaces bp,q,s, 0 &lt; p &lt; 1
    Edmunds, David E.
    Evans, W. Desmond
    Karadzhov, Gyorgi E.
    REVISTA MATEMATICA COMPLUTENSE, 2007, 20 (02): : 445 - 462
  • [3] Radial Time-Frequency Analysis and Embeddings of Radial Modulation Spaces
    Holger Rauhut
    Sampling Theory in Signal and Image Processing, 2006, 5 (2): : 201 - 224
  • [4] Time-frequency analysis with the q-Gaussian W transform
    de Souza, D. C. C.
    de Lima, P. D. S.
    de Araujo, J. M.
    Corso, G.
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2025, 665
  • [5] CONVOLUTION INEQUALITIES IN WEIGHTED LORENTZ SPACES: CASE 0 &lt; q &lt; 1
    Krepela, Martin
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2017, 20 (01): : 191 - 201
  • [6] Duality for logarithmic interpolation spaces when 0 &lt; q &lt; 1 and applications
    Besoy, Blanca F.
    Cobos, Fernando
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 466 (01) : 373 - 399
  • [7] Hypersingular integral operators on modulation spaces for 0 &lt; p &lt; 1
    Cheng, Meifang
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
  • [8] Translation-invariant operators on Lorentz spaces L(1,q) with 0&lt;q&lt;1
    Colzani, L
    Sjögren, P
    STUDIA MATHEMATICA, 1999, 132 (02) : 101 - 124
  • [9] Operators from HP to lq for 0 &lt;p &lt;1&lt;q &lt;∞
    Blasco, Oscar
    Function Spaces, 2007, 435 : 81 - 87
  • [10] Some results on Q(p) spaces, 0<p<1
    Essen, M
    Xiao, J
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1997, 485 : 173 - 195
12345