We study continuous measures on a compact semisimple Lie group using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if is a compact set of continuous measures on there exists a singular measure such that is absolutely continuous with respect to the Haar measure on for every in . In Section 4 we show that if is a finite linear combination of characters then there exist two singular measures and on such that . In the final section we obtain a Wiener-type characterization of a continuous measure on a symmetric space of compact type .
On étudie des mesures continues sur un groupe de Lie compact semi-simple en utilisant la théorie des représentations. À la section 2 nous donnons une caractérisation des mesures continues sur analogue à celle de Wiener pour le groupe du cercle. Puis on construit des mesures sur qui sont liées aux produits de Riesz sur les groupes abéliens localement compacts. En utilisant cette mesure on montre à la section 3 que si est une partie compacte des mesures continues sur , il existe une mesure singulière telle que la mesure soit absolument continue par rapport à la mesure de Haar sur pour toute mesure dans . À la section 4 on montre que si est une combinaison linéaire finie de caractères, il existe deux mesures singulières et sur telles que . À la section 5 on donne une caractérisation des mesures continues sur un espace symétrique compact .
@article{AIF_2000__50_4_1277_0, author = {Anoussis, M. and Bisbas, A.}, title = {Continuous measures on compact {Lie} groups}, journal = {Annales de l'Institut Fourier}, pages = {1277--1296}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {4}, year = {2000}, doi = {10.5802/aif.1793}, mrnumber = {2001m:43020}, zbl = {0969.43001}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1793/} }
TY - JOUR AU - Anoussis, M. AU - Bisbas, A. TI - Continuous measures on compact Lie groups JO - Annales de l'Institut Fourier PY - 2000 SP - 1277 EP - 1296 VL - 50 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1793/ DO - 10.5802/aif.1793 LA - en ID - AIF_2000__50_4_1277_0 ER -
%0 Journal Article %A Anoussis, M. %A Bisbas, A. %T Continuous measures on compact Lie groups %J Annales de l'Institut Fourier %D 2000 %P 1277-1296 %V 50 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1793/ %R 10.5802/aif.1793 %G en %F AIF_2000__50_4_1277_0
Anoussis, M.; Bisbas, A. Continuous measures on compact Lie groups. Annales de l'Institut Fourier, Volume 50 (2000) no. 4, pp. 1277-1296. doi : 10.5802/aif.1793. http://archive.numdam.org/articles/10.5802/aif.1793/
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