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arXiv · 0912.3129

A characterization of Fourier transforms

Philippe Jaming
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Abstract

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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Philippe Jaming. 2009-12-16. A characterization of Fourier transforms. https://arxiv.org/abs/0912.3129

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