[Mesures continues sur des espaces homogènes]
Dans ce travail, on étend la caractérisation des mesures continues, due à Wiener, à des variétés compactes et homogènes. Pour des groupes de Lie compacts et semisimples, et pour des nilvariétés, on trouve des conditions nécessaires et suffisantes pour qu’une mesure de probabilité soit continue. Les démonstrations s’appuient sur des propriétés élémentaires des noyaux de la chaleur.
In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.
Keywords: Probability measures on groups, heat kernels
Mot clés : mesures de probabilités sur des groupes, noyaux de chaleur
@article{AIF_2009__59_6_2169_0,
author = {Bj\"orklund, Michael and Fish, Alexander},
title = {Continuous {Measures} on {Homogenous} {Spaces}},
journal = {Annales de l'Institut Fourier},
pages = {2169--2174},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {59},
number = {6},
year = {2009},
doi = {10.5802/aif.2487},
zbl = {1194.60009},
mrnumber = {2640917},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2487/}
}
TY - JOUR AU - Björklund, Michael AU - Fish, Alexander TI - Continuous Measures on Homogenous Spaces JO - Annales de l'Institut Fourier PY - 2009 SP - 2169 EP - 2174 VL - 59 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2487/ DO - 10.5802/aif.2487 LA - en ID - AIF_2009__59_6_2169_0 ER -
%0 Journal Article %A Björklund, Michael %A Fish, Alexander %T Continuous Measures on Homogenous Spaces %J Annales de l'Institut Fourier %D 2009 %P 2169-2174 %V 59 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2487/ %R 10.5802/aif.2487 %G en %F AIF_2009__59_6_2169_0
Björklund, Michael; Fish, Alexander. Continuous Measures on Homogenous Spaces. Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2169-2174. doi : 10.5802/aif.2487. http://www.numdam.org/articles/10.5802/aif.2487/
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