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CONVOLUTIONS OF GENERIC ORBITAL MEASURES IN COMPACT SYMMETRIC SPACES

Part of: Abstract harmonic analysis Global differential geometry

Published online by Cambridge University Press:  05 May 2009

SANJIV KUMAR GUPTA  and
KATHRYN E. HARE
SANJIV KUMAR GUPTA
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, PO Box 36, Al Khodh 123, Sultanate of Oman (email: gupta@squ.edu.om)
KATHRYN E. HARE*
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 (email: kehare@uwaterloo.ca)
*
✉For correspondence; e-mail: kehare@uwaterloo.ca
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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,a2∈G 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.

Keywords

compact symmetric spacedouble cosetabsolutely continuous measure

MSC classification

Secondary: 43A80: Analysis on other specific Lie groups 53C35: Symmetric spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 513 - 522
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

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

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