• Segal-Bargmann Transform and Paley-Wiener Theorems on $M(2)$

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/120/02/0169-0183

• # Keywords

Segal–Bargmann transform; Poisson integrals; Paley–Wiener theorem.

• # 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.

• # Author Affiliations

1. Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019