Harmonic analysis on Heisenberg--Clifford Lie supergroups

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.

28 pages

Cited by in corpus (4)

• Superorbits
• Noncommutative Supergeometry and Quantum Supergroups
• $C^{\ast }$-algebras and direct integral decomposition for Lie supergroups
• Fréchet globalisations of Harish-Chandra supermodules