arXiv 1102.44752011-02-22math.RT

Harmonic analysis on Heisenberg--Clifford Lie supergroups

Alexander Alldridge, Joachim Hilgert, Martin Laubinger

备注：: 28 pages
发表信息：: J. London Math. Soc. 87 (2013), no. 2, 561-585
DOI：: 10.1112/jlms/jds058

英文摘要：

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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