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.
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页码：564 / 574
页数：11
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