Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

被引：16
|
作者：
Radha, R. [2 ]
Thangavelu, S. [1 ]
机构：
[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India
[2] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 354卷 / 02期
关键词：
Bargmann transform; Hermite functions; Hermite semigroup; Special Hermite functions; Short term Fourier transform; Sobolev space; SEGAL-BARGMANN TRANSFORM;
D O I：
10.1016/j.jmaa.2009.01.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：564 / 574
页数：11
相关论文
共 50 条
  • [21] Real Paley-Wiener theorems for the Clifford Fourier transform
    Fu YingXiong
    Li LuoQing
    SCIENCE CHINA-MATHEMATICS, 2014, 57 (11) : 2381 - 2392
  • [22] Real Paley-Wiener theorems for the Clifford Fourier transform
    FU YingXiong
    LI LuoQing
    ScienceChina(Mathematics), 2014, 57 (11) : 2381 - 2392
  • [23] Paley-Wiener and Boas Theorems for the Quaternion Fourier Transform
    Yingxiong Fu
    Luoqing Li
    Advances in Applied Clifford Algebras, 2013, 23 : 837 - 848
  • [24] A REAL PALEY-WIENER THEOREM FOR THE GENERALIZED DUNKL TRANSFORM
    Abouelaz, A.
    Achak, A.
    Daher, R.
    Loualid, El.
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2015, 8 (02): : 87 - 92
  • [25] ON GENERALIZATION OF PALEY-WIENER THEOREM FOR WEIGHTED HARDY SPACES
    Vinnitskii, B. V.
    Dilnyi, V. N.
    UFA MATHEMATICAL JOURNAL, 2013, 5 (04): : 30 - 36
  • [26] TOWARDS A PALEY-WIENER THEOREM FOR SEMISIMPLE SYMMETRICAL SPACES
    DELORME, P
    FLENSTEDJENSEN, M
    ACTA MATHEMATICA, 1991, 167 (1-2) : 127 - 151
  • [27] A Paley-Wiener theorem for distributions on reductive symmetric spaces
    Van den Ban, E. P.
    Schlichtkrull, H.
    JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2007, 6 (04) : 557 - 577
  • [28] Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform
    Kou, Kit-Ian
    Xu, Rui-Hui
    Zhang, Yan-Hui
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2012, 35 (17) : 2122 - 2132
  • [29] Paley-Wiener Theorem for a Generalized Fourier Transform Associated to a Dunkl-Type Operator
    Fei, Minggang
    Yang, Lan
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
  • [30] A local Paley-Wiener theorem for compact symmetric spaces
    Olafsson, Gestur
    Schlichtkrull, Henrik
    ADVANCES IN MATHEMATICS, 2008, 218 (01) : 202 - 215
12345