Convolution of orbital measures in symmetric spaces

نتاج البحث: المساهمة في مجلةArticleمراجعة النظراء

3 اقتباسات (Scopus)


Let G/K be a noncompact symmetric space, Gc/K its compact dual, g = t ⊕ p the Cartan decomposition of the Lie algebra g of G, a a maximal abelian subspace of a, H be an element of a, a=exp (H) , and ac =exp (iH). In this paper, we prove that if for some positive integer r, v acr is absolutely continuous with respect to the Haar measure on Gc, then vra is absolutely continuous with respect to the left Haar measure on G, where ac (respectively a) is the K-bi-invariant orbital measure supported on the double coset KacK (respectively KaK). We also generalize a result of Gupta and Hare ['Singular dichotomy for orbital measures on complex groups', Boll.Unione Mat.Ital.(9)III(2010), 409-419] to general noncompact symmetric spaces and transfer many of their results from compact symmetric spaces to their dual noncompact symmetric spaces.

اللغة الأصليةEnglish
الصفحات (من إلى)470-485
عدد الصفحات16
دوريةBulletin of the Australian Mathematical Society
مستوى الصوت83
رقم الإصدار3
المعرِّفات الرقمية للأشياء
حالة النشرPublished - يونيو 2011

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