Fourier analysis on the Heisenberg group. I. Schwartz space |
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Authors: | Daryl Geller |
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Institution: | Department of Mathematics, University of Chicago, Chicago, Illinois 60637 USA |
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Abstract: | We derive a usable characterization of the group FT (Fourier Transform) of Schwartz space on the Heisenberg group n, in terms of certain asymptotic series. To accomplish this we study in detail the FT of multiplication and differentiation operators on n, the relation of multiple Fourier series to the FT, and the process of group contraction on n. We use our characterization to solve a form of the division problem for convolution of n, which has application to Hardy space theory. |
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