Convolutions of generic orbital measures in compact symmetric spaces

Sanjiv Kumar Gupta; Kathryn E. Hare

doi:10.1017/S0004972709000148

Convolutions of generic orbital measures in compact symmetric spaces

Sanjiv Kumar Gupta, Kathryn E. Hare

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We prove that in any compact symmetric space, G/K, there is a dense set of a1,a2G such that if j=mKajmk is the K-bi-invariant measure supported on KajK, then 12 is absolutely continuous with respect to Haar measure on G. Moreover, the product of double cosets, Ka1Ka2K, has nonempty interior in G.

Original language	English
Pages (from-to)	513-522
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	79
Issue number	3
DOIs	https://doi.org/10.1017/S0004972709000148
Publication status	Published - Jun 2009

Keywords

absolutely continuous measure
compact symmetric space
double coset

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S0004972709000148

Cite this

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abstract = "We prove that in any compact symmetric space, G/K, there is a dense set of a1,a2G such that if j=mKajmk is the K-bi-invariant measure supported on KajK, then 12 is absolutely continuous with respect to Haar measure on G. Moreover, the product of double cosets, Ka1Ka2K, has nonempty interior in G.",

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AB - We prove that in any compact symmetric space, G/K, there is a dense set of a1,a2G such that if j=mKajmk is the K-bi-invariant measure supported on KajK, then 12 is absolutely continuous with respect to Haar measure on G. Moreover, the product of double cosets, Ka1Ka2K, has nonempty interior in G.

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KW - compact symmetric space

KW - double coset

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Convolutions of generic orbital measures in compact symmetric spaces

Abstract

Keywords

ASJC Scopus subject areas

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