Harmonic analysis on Heisenberg--Clifford Lie supergroups

Details Harmonic analysis on Heisenberg--Clifford Lie supergroups Harmonic analysis on Heisenberg--Clifford Lie supergroups

2011-02-22

arxiv.org/abs/1102.4475v1

Mathematics

Representation Theory

28 pages

Scientific paper

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.

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