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

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

2009-05-18

arxiv.org/abs/0905.2802v1

Mathematics

Functional Analysis

Scientific paper

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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