English

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

Functional Analysis 2009-05-19 v1

Abstract

We study the Segal-Bargmann transform on M(2).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).M(2). We also prove a Paley-Wiener theorem for the inverse Fourier transform

Keywords

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}
}
R2 v1 2026-06-21T13:03:13.072Z