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Convolution of Orbital Measures on Symmetric Spaces of type Cp and Dp

Abstract :

We study the absolute continuity of the convolution δ♮eX⋆δ♮eY of two orbital measures on the symmetric spaces SO0(p,p)/SO(p)×SO(p), SU(p,p)/S(U(p)×U(p)) and Sp(p,p)/Sp(p)×Sp(p). We prove sharp conditions on X, Y∈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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Contributor : Okina Université d'Angers <>
Submitted on : Friday, November 4, 2016 - 10:10:29 AM
Last modification on : Monday, March 9, 2020 - 6:16:06 PM

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Piotr Graczyk, Peter Sawyer. Convolution of Orbital Measures on Symmetric Spaces of type Cp and Dp. Journal of the Australian Mathematical Society, Cambridge University Press, 2015, 98 (02), pp.232-256. ⟨10.1017/S1446788714000494⟩. ⟨hal-01392101⟩

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