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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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|
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