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.
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.
Accepted:
DOI: 10.5802/aif.2487
Classification: 60Bxx, 60B15, 30Cxx, 30C40
Keywords: Probability measures on groups, heat kernels
@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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.2487/} }
TY - JOUR TI - Continuous Measures on Homogenous Spaces JO - Annales de l'Institut Fourier PY - 2009 DA - 2009/// SP - 2169 EP - 2174 VL - 59 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2487/ UR - https://zbmath.org/?q=an%3A1194.60009 UR - https://www.ams.org/mathscinet-getitem?mr=2640917 UR - https://doi.org/10.5802/aif.2487 DO - 10.5802/aif.2487 LA - en ID - AIF_2009__59_6_2169_0 ER -
Björklund, Michael; Fish, Alexander. Continuous Measures on Homogenous Spaces. Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2169-2174. doi : 10.5802/aif.2487. https://aif.centre-mersenne.org/articles/10.5802/aif.2487/
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