Geodesic
A characterization of Fourier transforms
Philippe Jaming1
1 Université d'Orléans Faculté des Sciences MAPMO - Fédération Denis Poisson BP 6759 F 45067 Orléans Cedex 2, France
Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 569-580

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\mathbb Z}/ n{\mathbb Z}$, the integers ${\mathbb Z}$, the torus ${\mathbb T}$ and the real line. We also ask a related question for the twisted convolution.
DOI : 10.4064/cm118-2-12
Keywords: paper various situations only continuous linear map transforms convolution product pointwise product fourier transform focus cyclic groups mathbb mathbb integers mathbb torus mathbb real line ask related question twisted convolution

Philippe Jaming 1

1 Université d'Orléans Faculté des Sciences MAPMO - Fédération Denis Poisson BP 6759 F 45067 Orléans Cedex 2, France 
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Philippe Jaming. A characterization of Fourier transforms. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 569-580. doi: 10.4064/cm118-2-12

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