A characterization of Fourier transforms

Philippe Jaming

Published 2009-12-16Version 1

The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups $\Z/nZ$, the integers $\Z$, the Torus $\T$ and the real line. We also ask a related question for the twisted convolution.