Si est une fonction moyenne périodique, tempérée, sur le groupe d’Heisenberg réduit, alors le sous-espace fermé engendré par , invariant par translation et rotation, contient une fonction sphérique élémentaire. À l’aide d’un théorème de Paley-Wiener pour la transformation de Fourier-Weyl, nous formulons une conjecture pour les fonctions moyenne périodiques quelconques.
We show that when is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.
@article{AIF_1995__45_4_1007_0,
author = {Thangavelu, Sundaram},
title = {Mean periodic functions on phase space and the {Pompeiu} problem with a twist},
journal = {Annales de l'Institut Fourier},
pages = {1007--1035},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {45},
number = {4},
year = {1995},
doi = {10.5802/aif.1482},
mrnumber = {96m:43009},
zbl = {0831.43003},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.1482/}
}
TY - JOUR AU - Thangavelu, Sundaram TI - Mean periodic functions on phase space and the Pompeiu problem with a twist JO - Annales de l'Institut Fourier PY - 1995 SP - 1007 EP - 1035 VL - 45 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1482/ DO - 10.5802/aif.1482 LA - en ID - AIF_1995__45_4_1007_0 ER -
%0 Journal Article %A Thangavelu, Sundaram %T Mean periodic functions on phase space and the Pompeiu problem with a twist %J Annales de l'Institut Fourier %D 1995 %P 1007-1035 %V 45 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1482/ %R 10.5802/aif.1482 %G en %F AIF_1995__45_4_1007_0
Thangavelu, Sundaram. Mean periodic functions on phase space and the Pompeiu problem with a twist. Annales de l'Institut Fourier, Tome 45 (1995) no. 4, pp. 1007-1035. doi : 10.5802/aif.1482. http://archive.numdam.org/articles/10.5802/aif.1482/
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