On the product formula on noncompact Grassmannians

• Autorzy: Piotr Graczyk , Patrice Sawyer
• Języki publikacji: EN

Abstrakty

EN

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 ∈ 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 $δ_{e^X}^♮$.

Kategorie tematyczne

• 43A90: Spherical functions
• 53C35: Symmetric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 133
• Numer: 2
• Strony: 145-167

Daty

wydano

2013

Twórcy

autor

Piotr Graczyk

• Laboratoire de Mathématiques LAREMA, Université d'Angers, 49045 Angers, France

autor

Patrice Sawyer

• Department of Mathematics and Computer Science, Laurentian University, P3E 2C6 Sudbury, Ontario, Canada

Identyfikatory

DOI

10.4064/cm133-2-1