Absolute continuity of convolutions of orbital measures on Riemannian symmetric spaces
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.