A characterization of Fourier transforms

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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https://hal.archives-ouvertes.fr/hal-00441479
Contributor : Philippe Jaming <>
Submitted on : Wednesday, December 16, 2009 - 10:50:33 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, June 17, 2010 - 11:44:50 PM

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• HAL Id : hal-00441479, version 1
• ARXIV : 0912.3129

Citation

Philippe Jaming. A characterization of Fourier transforms. Colloquium Mathematicum, 2010, 118, pp.569-580. ⟨hal-00441479⟩

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