The smoothness of convolutions of singular orbital measures on complex grassmannians

Sanjiv Kumar Gupta, Kathryn E. Hare*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

ملخص

It is well known that if G/K is any irreducible symmetric space and μa is a continuous orbital measure supported on the double coset KaK, then the convolution product, μk a, is absolutely continuous for some suitably large k ≤ dimG/K. The minimal value of k is known in some symmetric spaces and in the special case of compact groups or rank one compact symmetric spaces it has even been shown that μk a belongs to the smaller space L2 for some k . Here we prove that this L2 property holds for all the compact, complex Grassmannian symmetric spaces, SU(p + q)/S(U(p) × U(q)) . Moreover, for the orbital measures at a dense set of points a, we prove that μ2 a ϵ L2 (or μ3 a ϵ L2 if p = q ).

اللغة الأصليةEnglish
الصفحات (من إلى)335-349
عدد الصفحات15
دوريةJournal of Lie Theory
مستوى الصوت31
رقم الإصدار2
حالة النشرPublished - 2021
منشور خارجيًانعم

ASJC Scopus subject areas

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