[Un théorème de Paley-Wiener spectral pour le groupe d’Heisenberg et un théorème de support pour les moyennes shériques tordues sur ]
Nous prouvons un théorème de Paley-Wiener spectral pour le groupe d’Heisenberg en utilisant un théorème du support pour les moyennes sphériques tordues sur Si est une fonction dans la classe de Schwartz nous montrons que a un support dans une boule de de rayon si et seulement si pour et pour tout C’est un analogue du théorème du support prouvé dans les contextes euclidiens et hyperboliques par Helgason. Lorsque nous montrons que les deux conditions pour impliquent un théorème du support pour une grande classe de fonctions à croissance exponentielle. Il est surprenant de constater que ce dernier résultat ne se généralise pas aux dimensions supérieures.
We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on If is a Schwartz class function we show that is supported in a ball of radius in if and only if for for all This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When we show that the two conditions for imply a support theorem for a large class of functions with exponential growth. Surprisingly enough,this latter result does not generalize to higher dimensions.
Mots clés : Spectral Paley-Wiener theorem, twisted spherical means, special Hermite operator, Laguerre functions, support theorem, spherical harmonics
@article{AIF_2006__56_2_459_0, author = {Narayanan, E.~K. and Thangavelu, S.}, title = {A spectral {Paley-Wiener} theorem for the {Heisenberg} group and a support theorem for the twisted spherical means on $\mathbb{C}^n$}, journal = {Annales de l'Institut Fourier}, pages = {459--473}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {2}, year = {2006}, doi = {10.5802/aif.2189}, zbl = {1089.43006}, mrnumber = {2226023}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2189/} }
TY - JOUR AU - Narayanan, E. K. AU - Thangavelu, S. TI - A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on $\mathbb{C}^n$ JO - Annales de l'Institut Fourier PY - 2006 SP - 459 EP - 473 VL - 56 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2189/ DO - 10.5802/aif.2189 LA - en ID - AIF_2006__56_2_459_0 ER -
%0 Journal Article %A Narayanan, E. K. %A Thangavelu, S. %T A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on $\mathbb{C}^n$ %J Annales de l'Institut Fourier %D 2006 %P 459-473 %V 56 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2189/ %R 10.5802/aif.2189 %G en %F AIF_2006__56_2_459_0
Narayanan, E. K.; Thangavelu, S. A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on $\mathbb{C}^n$. Annales de l'Institut Fourier, Tome 56 (2006) no. 2, pp. 459-473. doi : 10.5802/aif.2189. http://www.numdam.org/articles/10.5802/aif.2189/
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