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Article Dans Une Revue Colloquium Mathematicum Année : 2013

On the product formula on noncompact Grassmannians

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Résumé

We study the absolute continuity of the convolution δ♮eX⋆δ♮eY of two orbital measures on the symmetric space SO0(p,q)/SO(p)×SO(q), q>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. 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 absolute continuity of convolution powers of an orbital measure δ♮eX.

Dates et versions

hal-03038379 , version 1 (03-12-2020)

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Piotr Graczyk, Patrice Sawyer. On the product formula on noncompact Grassmannians. Colloquium Mathematicum, 2013, 133 (2), pp.145-167. ⟨10.4064/cm133-2-1⟩. ⟨hal-03038379⟩
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