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Article Dans Une Revue Journal of Functional Analysis Année : 2010

Absolute continuity of convolutions of orbital measures on Riemannian symmetric spaces

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Résumé

We study the absolute continuity of the measures δeX1δeXm and of (δeX)l on the Riemannian symmetric spaces X of noncompact type for nonzero elements XjXj, XaXa. For m,lr+1m,lr+1, where r is the rank of X, the considered convolutions have a density. We conjecture that the condition m,lr+1m,lr+1 is necessary. The conjecture is proved for the symmetric spaces of type An−1An−1. Moreover, the minimal value of l is determined, in function of the irregularity of X.

Dates et versions

hal-03040202 , version 1 (04-12-2020)

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Piotr Graczyk, Patrice Sawyer. Absolute continuity of convolutions of orbital measures on Riemannian symmetric spaces. Journal of Functional Analysis, 2010, 259 (7), pp.1759 - 1770. ⟨10.1016/j.jfa.2010.05.017⟩. ⟨hal-03040202⟩
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