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

Radha ., R and Thangavelu, S (2009) Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform. In: Journal of Mathematical Analysis and Applications, 354 (2). pp. 564-574.

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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 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.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Bargmann transform; Hermite functions; Hermite semigroup; Special Hermite functions; Short term Fourier transform; Sobolev space
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Mar 2010 06:34
Last Modified: 19 Sep 2010 05:56
URI: http://eprints.iisc.ernet.in/id/eprint/26045

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