A characterisation of the fourier transform on the heisenberg group

Abstract

The aim of this paper is to show that any continuous *-homomorphism of L1(Cn)(with twisted convolution as multiplication) into B(L2(Rn)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution. © 2012, Duke University Press. All rights reserved.