[Une caractérisation de la transformation de Fourier et questions connexes]
On montre que la transformation de Fourier est essentiellement, à une simple adaptation près, la seule application, qui sur les espaces où elle opère, transforme les convolutions en produits et les produits en convolutions. (De manière surprenante la linéarité n'est pas supposée à priori.)
It is shown that the Fourier transform is essentially, up to a simple adjustment, the only transform on the corresponding space which maps convolutions to products and products to convolutions (surprisingly, no linearity is assumed a priori).
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@article{CRMATH_2008__346_11-12_625_0,
author = {Alesker, Semyon and Artstein-Avidan, Shiri and Milman, Vitali},
title = {A characterization of the {Fourier} transform and related topics},
journal = {Comptes Rendus. Math\'ematique},
pages = {625--628},
publisher = {Elsevier},
volume = {346},
number = {11-12},
year = {2008},
doi = {10.1016/j.crma.2008.04.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.04.001/}
}
TY - JOUR AU - Alesker, Semyon AU - Artstein-Avidan, Shiri AU - Milman, Vitali TI - A characterization of the Fourier transform and related topics JO - Comptes Rendus. Mathématique PY - 2008 SP - 625 EP - 628 VL - 346 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.04.001/ DO - 10.1016/j.crma.2008.04.001 LA - en ID - CRMATH_2008__346_11-12_625_0 ER -
%0 Journal Article %A Alesker, Semyon %A Artstein-Avidan, Shiri %A Milman, Vitali %T A characterization of the Fourier transform and related topics %J Comptes Rendus. Mathématique %D 2008 %P 625-628 %V 346 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.04.001/ %R 10.1016/j.crma.2008.04.001 %G en %F CRMATH_2008__346_11-12_625_0
Alesker, Semyon; Artstein-Avidan, Shiri; Milman, Vitali. A characterization of the Fourier transform and related topics. Comptes Rendus. Mathématique, Tome 346 (2008) no. 11-12, pp. 625-628. doi : 10.1016/j.crma.2008.04.001. http://www.numdam.org/articles/10.1016/j.crma.2008.04.001/
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Cité par Sources :
⁎ The research was supported in part by Israel Science Foundation: first named author by grant No. 1369/04, second named author by grant No. 865/07, third named author by grant No. 491/04. The second and third names authors were supported in part by BSF grant No. 2006079.
