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

Abstract : We study the absolute continuity of the convolution $\delta_{e^X}^\natural \star\delta_{e^Y}^\natural$ of two orbital measures on the symmetric spaces ${\bf SO}_0(p,p)/{\bf SO}(p)\times{\bf SO}(p)$, $\SU(p,p)/{\bf S}({\bf U}(p)\times{\bf U}(p))$ 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.
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https://hal.archives-ouvertes.fr/hal-00965263
Contributor : Piotr Graczyk Connect in order to contact the contributor
Submitted on : Monday, March 24, 2014 - 8:23:00 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:50 AM
Long-term archiving on: : Tuesday, June 24, 2014 - 12:57:04 PM

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### Identifiers

• HAL Id : hal-00965263, version 1
• ARXIV : 1403.6098

### Citation

Piotr Graczyk, Patrice Sawyer. Convolution of orbital measures on symmetric spaces of type $C_p$ and $D_p$. 2014. ⟨hal-00965263⟩

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