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

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      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

       

      E K Narayanan1 Suparna Sen1

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

       
  • Proceedings – Mathematical Sciences | News

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