Continuous Measures on Homogenous Spaces
[Mesures continues sur des espaces homogènes]
Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2169-2174.

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.

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)
@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/

[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

Cité par Sources :