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Segal-Bargmann transform and Paley-Wiener theorems on M(2)

Narayanan, EK and Sen, Suparna (2010) Segal-Bargmann transform and Paley-Wiener theorems on M(2). In: Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 120 (2). pp. 169-183.

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Abstract

We study the Segal-Bargmann transform on M(2). The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are investigated. Using a Gutzmer's type formula we characterize the range as a class of functions extending holomorphically to an appropriate domain in the complexification of M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Indian Academy of Sciences.
Keywords: Segal-Bargmann transform; Poisson integrals; Paley-Wiener theorem.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 20 Sep 2010 09:08
Last Modified: 20 Sep 2010 09:08
URI: http://eprints.iisc.ernet.in/id/eprint/32246

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