A characterization of Fourier transforms

Details A characterization of Fourier transforms A characterization of Fourier transforms

2009-12-16

arxiv.org/abs/0912.3129v1

Mathematics

Classical Analysis and ODEs

In memory of A. Hulanicki

Scientific paper

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.

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