A characterization of Fourier transforms

Volume 118 / 2010

Philippe Jaming Colloquium Mathematicum 118 (2010), 569-580 MSC: 42A38, 42A85, 42B10, 43A25. DOI: 10.4064/cm118-2-12

Abstract

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.

Authors

  • Philippe JamingUniversité d'Orléans
    Faculté des Sciences
    MAPMO - Fédération Denis Poisson
    BP 6759
    F 45067 Orléans Cedex 2, France
    e-mail

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