Segal-Bargmann transform and Paley-Wiener theorems on M(2)
- 72 Downloads
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.
KeywordsSegal-Bargmann transform Poisson integrals Paley-Wiener theorem
Unable to display preview. Download preview PDF.