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
Mot clés : mesures de probabilités sur des groupes, noyaux de chaleur
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/

[1] Anker, Jean-Philippe; Ostellari, Patrick The heat kernel on noncompact symmetric spaces. Lie groups and symmetric spaces, Amer. Math. Soc. Transl. Ser. 2, Volume 210 (2003), pp. 27-46 (Providence, RI) | MR | Zbl

[2] Anoussis, M.; Bisbas, A. Continuous measures on compact Lie groups, Ann. Inst. Fourier (Grenoble), Volume 50 (2000) no. 4, pp. 1277-1296 | DOI | Numdam | MR | Zbl

[3] Berger, M A panoramic view of Riemannian geometry, Springer-Verlag, Berlin, 2003 (xxiv+824 pp. ISBN: 3-540-65317-1) | MR | Zbl

[4] Chavel, I. Riemannian Geometry: A Modern Introduction, Cambridge University Press, New York, 1994 | MR | Zbl

[5] Deninger, C.; Singhof, W. The e-invariant and the spectrum for compact nilmanifolds covered by Heisenberg groups, Invent. Math., Volume 78 (1984), pp. 101-112 | DOI | MR | Zbl

[6] Fegan, H.D. The heat equation on a compact Lie group, Trans. Amer. Math. Soc., Volume 246 (1978), pp. 339-357 | DOI | MR | Zbl

[7] Graham, C. C.; McGehee, O. C. Essays in Commutative Harmonic Analysis, Springer-Verlag, New York, 1979 | MR | Zbl

[8] Taylor, M. Noncommutative Harmonic Analysis, Math. Surveys and Monogr, American Math. Society, Providence, R.I., 1986 no. 22 | MR | Zbl

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