The aim of this paper is to show that, in various situations, the only continuous linear (or not) 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-12,
author = {Philippe Jaming},
title = {A characterization of Fourier transforms},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {569-580},
zbl = {1193.43004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-12}
}
Philippe Jaming. A characterization of Fourier transforms. Colloquium Mathematicae, Tome 120 (2010) pp. 569-580. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-12/