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Currently displaying 1 – 3 of 3

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The product formula for the spherical functions on symmetric spaces of noncompact type.

Graczyk, Piotr; Sawyer, Patrice — 2003

Journal of Lie Theory

On connections, geodesics and sprays in synthetic differential geometry

Marta Bunge; Patrice Sawyer — 1984

Cahiers de Topologie et Géométrie Différentielle Catégoriques

On the product formula on noncompact Grassmannians

Piotr Graczyk; Patrice Sawyer — 2013

Colloquium Mathematicae

We study the absolute continuity of the convolution $δ_{e^{X}}^{♮} * δ_{e^{Y}}^{♮}$ of two orbital measures on the symmetric space SO₀(p,q)/SO(p)×SO(q), q > p. We prove sharp conditions on X,Y ∈ for the existence of the density of the convolution measure. This measure intervenes in the product formula for the spherical functions. We show that the sharp criterion developed for SO₀(p,q)/SO(p)×SO(q) also serves for the spaces SU(p,q)/S(U(p)×U(q)) and Sp(p,q)/Sp(p)×Sp(q), q > p. We moreover apply our results to the study of...

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