Convolution of orbital measures on symmetric spaces of type $C_p$ and $D_p$

Abstract

We study the absolute continuity of the convolution ${\delta }_{e^X}^{♮}\star {\delta }_{e^Y}^{♮}$ of two orbital measures on the symmetric spaces ${\mathbf{SO}}_0(p,p)/\mathbf{SO}(p)\times \mathbf{SO}(p)$, $\SU(p,p)/{\bf S}({\bf U}(p)\times{\bf U}(p))$ and $\Sp(p,p)/{\bf Sp }(p)\times\Sp(p)$. We prove sharp conditions on $X$, $Y\in\a$ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions.

arXiv admin note: text overlap with arXiv:1212.0002

Cited by in corpus (1)

• The smoothness of orbital measures on noncompact symmetric spaces