Nous montrons que, sous certaines conditions, la transformation de Fourier est complétement charactérisée par la formule sommatoire de Poisson. Nous proposons aussi une transformation généralisée qui est dérivée d'une formule de sommation de type Poisson ; nous l'appelons la transformation de Fourier–Poisson.
We show that, under certain conditions, the Fourier transform is completely characterized by Poisson's summation formula. Also, we propose a generalized transform which is derived from a Poisson-type summation formula, that we call a Fourier–Poisson transform.
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@article{CRMATH_2010__348_7-8_407_0, author = {Faifman, Dmitry}, title = {A characterization of {Fourier} transform by {Poisson} summation formula}, journal = {Comptes Rendus. Math\'ematique}, pages = {407--410}, publisher = {Elsevier}, volume = {348}, number = {7-8}, year = {2010}, doi = {10.1016/j.crma.2010.01.023}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.01.023/} }
TY - JOUR AU - Faifman, Dmitry TI - A characterization of Fourier transform by Poisson summation formula JO - Comptes Rendus. Mathématique PY - 2010 SP - 407 EP - 410 VL - 348 IS - 7-8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.01.023/ DO - 10.1016/j.crma.2010.01.023 LA - en ID - CRMATH_2010__348_7-8_407_0 ER -
%0 Journal Article %A Faifman, Dmitry %T A characterization of Fourier transform by Poisson summation formula %J Comptes Rendus. Mathématique %D 2010 %P 407-410 %V 348 %N 7-8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.01.023/ %R 10.1016/j.crma.2010.01.023 %G en %F CRMATH_2010__348_7-8_407_0
Faifman, Dmitry. A characterization of Fourier transform by Poisson summation formula. Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 407-410. doi : 10.1016/j.crma.2010.01.023. http://archive.numdam.org/articles/10.1016/j.crma.2010.01.023/
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[2] On some infinite series involving arithmetical functions, Quart. J. Math., Volume 8 (1937) no. 8–13, pp. 313-320
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