Segal-Bargmann transform and Paley-Wiener theorems on $M(2).$
Functional Analysis
2009-05-19 v1
Abstract
We study the Segal-Bargmann transform on 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 We also prove a Paley-Wiener theorem for the inverse Fourier transform
Cite
@article{arxiv.0905.2802,
title = {Segal-Bargmann transform and Paley-Wiener theorems on $M(2).$},
author = {E. K. Narayanan and Suparna Sen},
journal= {arXiv preprint arXiv:0905.2802},
year = {2009}
}