Segal-Bargmann transform and Paley-Wiener theorems on <Emphasis Type="Italic">M</Emphasis>(2) |
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Authors: | E K Narayanan Suparna Sen |
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Institution: | 1.Department of Mathematics,Indian Institute of Science,Bangalore,India |
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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. |
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