Publicacions Matemàtiques

Revisiting the Fourier transform on the Heisenberg group

Abstract

A recent theorem of S. Alesker, S. Artstein-Avidan and V. Milman characterises the Fourier transform on ${\mathbb R}^{n}$ as essentially the only transform on the space of tempered distributions which interchanges convolutions and pointwise products. In this note we study the image of the Schwartz space on the Heisenberg group under the Fourier transform and obtain a similar characterisation for the Fourier transform on the Heisenberg group

Article information

Source
Publ. Mat., Volume 58, Number 1 (2014), 47-63.

Dates
First available in Project Euclid: 20 December 2013