TY - JOUR
T1 - Convolutions of generic orbital measures in compact symmetric spaces
AU - Gupta, Sanjiv Kumar
AU - Hare, Kathryn E.
PY - 2009/6
Y1 - 2009/6
N2 - 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.
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.
KW - absolutely continuous measure
KW - compact symmetric space
KW - double coset
UR - http://www.scopus.com/inward/record.url?scp=77957223361&partnerID=8YFLogxK
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U2 - 10.1017/S0004972709000148
DO - 10.1017/S0004972709000148
M3 - Article
AN - SCOPUS:77957223361
SN - 0004-9727
VL - 79
SP - 513
EP - 522
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 3
ER -