Holomorphic sobolev spaces, hermite and special hermite semigroups and a Paley-Wiener theorem for the windowed fourier transform

Radha, R. ; Thangavelu, S. (2009) Holomorphic sobolev spaces, hermite and special hermite semigroups and a Paley-Wiener theorem for the windowed fourier transform Journal of Mathematical Analysis and Applications, 354 (2). pp. 564-574. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jmaa.2009.01.021

Abstract

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 Rn and Cn 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.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Bargmann Transform; Hermite Functions; Hermite Semigroup; Special Hermite Functions; Short Term Fourier Transform; Sobolev Space
ID Code:53604
Deposited On:09 Aug 2011 11:42
Last Modified:09 Aug 2011 11:42

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