Fourier analysis on the Heisenberg group.
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.
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012.
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Geller