A characterization of Fourier transforms
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
@article{10_4064_cm118_2_12,
     author = {Philippe Jaming},
     title = {A characterization of {Fourier} transforms},
     journal = {Colloquium Mathematicum},
     pages = {569--580},
     publisher = {mathdoc},
     volume = {118},
     number = {2},
     year = {2010},
     doi = {10.4064/cm118-2-12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-12/}
}
TY  - JOUR
AU  - Philippe Jaming
TI  - A characterization of Fourier transforms
JO  - Colloquium Mathematicum
PY  - 2010
SP  - 569
EP  - 580
VL  - 118
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-12/
DO  - 10.4064/cm118-2-12
LA  - en
ID  - 10_4064_cm118_2_12
ER  - 
%0 Journal Article
%A Philippe Jaming
%T A characterization of Fourier transforms
%J Colloquium Mathematicum
%D 2010
%P 569-580
%V 118
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-12/
%R 10.4064/cm118-2-12
%G en
%F 10_4064_cm118_2_12
Philippe Jaming. A characterization of Fourier transforms. Colloquium Mathematicum, Tome 118 (2010) no. 2, pp. 569-580. doi : 10.4064/cm118-2-12. http://geodesic.mathdoc.fr/articles/10.4064/cm118-2-12/

Cité par Sources :