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Average under the Iwasawa transformation

Author(s): Ming Liao; Longmin Wang
Journal: Proc. Amer. Math. Soc. 135 (2007), 895-901.
MSC (2000): Primary 22E46; Secondary 43A80
Posted: August 28, 2006
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Abstract: We derive an averaging property under the Iwasawa decomposition on a semisimple Lie group of noncompact type based on a limiting property of random walks in the Lie group.

References:

1.: Y. Guivarc'h et A. Raugi, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Z. Wahrsch. verw. Gebiete 69 (1985), 187-242. MR 0779457 (86h:60126)
2.: S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Academic Press, 1978. MR 0514561 (80k:53081)
3.: B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. 6 (1973), 413-455. MR 0364552 (51:806)
4.: M. Liao, Lévy processes in Lie groups, Cambridge Univ. Press, 2004. MR 2060091 (2005e:60004)

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Additional Information:

Ming Liao
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email: liaomin@auburn.edu

Longmin Wang
Affiliation: Department of Mathematics, Nankai University, Tianjin, People's Republic of China
Email: wanglm@nankai.edu.cn

DOI: 10.1090/S0002-9939-06-08508-X
PII: S 0002-9939(06)08508-X
Keywords: Iwasawa decomposition
Received by editor(s): April 6, 2005
Received by editor(s) in revised form: September 27, 2005
Posted: August 28, 2006
Additional Notes: This paper was completed during the first author's visit to Nankai University and was supported by Nankai University.
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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