no. 6
Continuous Measures on Homogenous Spaces
Björklund, Michael1; Fish, Alexander2
1 Royal Institute of Technology (KTH) Department of Mathematics Lindstedtsvägen 25 S-100 44 Stockholm (Suède)
2 The Ohio State University Department of Mathematics 231 W. 18-th Ave., Columbus OH 43210 (USA)
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2169-2174.

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.

DOI: 10.5802/aif.2487
Classification: 60Bxx, 60B15, 30Cxx, 30C40
Keywords: Probability measures on groups, heat kernels
Björklund, Michael 1; Fish, Alexander 2

1 Royal Institute of Technology (KTH) Department of Mathematics Lindstedtsvägen 25 S-100 44 Stockholm (Suède)
2 The Ohio State University Department of Mathematics 231 W. 18-th Ave., Columbus OH 43210 (USA) 
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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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