A characterization of Fourier transforms

• Autorzy: Philippe Jaming
• Języki publikacji: EN

Abstrakty

EN

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 ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
• 42A85: Convolution, factorization
• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 569-580

Daty

wydano

2010

Twórcy

autor

Philippe Jaming

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

Identyfikatory

DOI

10.4064/cm118-2-12