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

2009/05/18 by Narayanan, E. K., Suparna Sen, Sen, Suparna
Mathematics · #Holomorphic and Operator Theory #Advanced Algebra and Geometry #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.0905.2802

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 studied. Using a Gutzmer 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

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