Proceedings - Mathematical Sciences

, Volume 120, Issue 2, pp 169–183 | Cite as

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

  • E. K. NarayananEmail author
  • Suparna Sen


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.


Segal-Bargmann transform Poisson integrals Paley-Wiener theorem 


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Copyright information

© Indian Academy of Sciences 2010

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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