Harmonic analysis on Heisenberg--Clifford Lie supergroups
Representation Theory
2013-04-16 v1
Abstract
We define a Fourier transform and a convolution product for functions and distributions on Heisenberg--Clifford Lie supergroups. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. We generalize various classical theorems, including the Paley--Wiener--Schwartz theorem, and define a convolution Banach algebra.
Cite
@article{arxiv.1102.4475,
title = {Harmonic analysis on Heisenberg--Clifford Lie supergroups},
author = {Alexander Alldridge and Joachim Hilgert and Martin Laubinger},
journal= {arXiv preprint arXiv:1102.4475},
year = {2013}
}
Comments
28 pages