Harmonic analysis on Heisenberg-Clifford Lie supergroups

What is it about?

We introduce a natural Fourier transform on the Heisenberg–Clifford Lie supergroup, covariant for the left regular representation. We prove a Fourier inversion formula, a Schwartz space isomorphism and Paley–Wiener–Schwartz theorem. The Fourier transform is an algebra homomorphism for a natural convolution product. This leads to the definition of convolution Banach algebra of Sobolev Wn1 type.

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