A characterization of Fourier transforms
Résumé
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.
Domaines
Analyse classique [math.CA]
Origine : Fichiers produits par l'(les) auteur(s)