The absolute continuity of convolutions of orbital measures in symmetric spaces

Sanjiv Kumar Gupta, Kathryn E. Hare*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةArticleمراجعة النظراء

2 اقتباسات (Scopus)


We characterize the absolute continuity of convolution products of orbital measures on the classical, irreducible Riemannian symmetric spaces G/K of Cartan type III, where G is a non-compact, connected Lie group and K is a compact, connected subgroup. By the orbital measures, we mean the uniform measures supported on the double cosets, KzK, in G. The characterization can be expressed in terms of dimensions of eigenspaces or combinatorial properties of the annihilating roots of the elements z. A consequence of our work is to show that the convolution product of any rank G/K, continuous, K-bi-invariant measures is absolutely continuous in any of these symmetric spaces, other than those whose restricted root system is type An or D3, when rank G/K +1 is needed.

اللغة الأصليةEnglish
الصفحات (من إلى)81-111
عدد الصفحات31
دوريةJournal of Mathematical Analysis and Applications
مستوى الصوت450
رقم الإصدار1
المعرِّفات الرقمية للأشياء
حالة النشرPublished - يونيو 1 2017

ASJC Scopus subject areas

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