Fourier analysis on the Heisenberg group
- 1 April 1977
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 74 (4) , 1328-1331
- https://doi.org/10.1073/pnas.74.4.1328
Abstract
We obtain a usable characterization of the (group) Fourier transform of (H(n)) (Schwartz space on the Heisenberg group). The characterization involves writing elements of [Formula: see text] as asymptotic series in Planck's constant. In the process, we derive a new "discrete" version of spherical harmonics, and elucidate the theory of group contractions. We give an application to Hardy space theory.Keywords
This publication has 1 reference indexed in Scilit:
- On the Contraction of Groups and Their RepresentationsProceedings of the National Academy of Sciences, 1953