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CONVOLUTIONS OF GENERIC ORBITAL MEASURES IN COMPACT SYMMETRIC SPACES

Published online by Cambridge University Press:  05 May 2009

SANJIV KUMAR GUPTA
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al Khodh 123, Sultanate of Oman (email: [email protected])
KATHRYN E. HARE*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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We prove that in any compact symmetric space, G/K, there is a dense set of a1,a2G such that if μj=mK*δaj*mk is the K-bi-invariant measure supported on KajK, then μ1*μ2 is absolutely continuous with respect to Haar measure on G. Moreover, the product of double cosets, Ka1Ka2K, has nonempty interior in G.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research was supported in part by NSERC and the Sultan Qaboos University.

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