Poisson transformations on affine symmetric spaces

DOI10.3792/pjaa.55.323zbMath0485.22011OpenAlexW2053870154MaRDI QIDQ1164164

Toshio Oshima

Publication date: 1979

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.55.323

zbMATH Keywords

Poisson integraleigenfunctionsemisimple Lie groupboundary valueaffine symmetric spaceSato's hyperfunction

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Differential geometry of symmetric spaces (53C35)

Related Items

The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors, Invariant subspaces of functions and the Poisson transformation for hyperboloids, Symmetry breaking for representations of rank one orthogonal groups, Characterization of the \(L^p\) range of a generalized Poisson transform of the hyperbolic space \(B(\mathbb{H}^n)\), Generalized Laplacians for generalized Poisson-Cauchy transforms on classical domains, Cohomologically induced distinguished representations and cohomological test vectors, ON S-HARDY–LITTLEWOOD HOMOGENEOUS SPACES, On some series of representations related to symmetric spaces, Zeta functions of prehomogeneous vector spaces with coefficients related to periods of automorphic forms

Cites Work

• Eigenspaces of invariant differential operators on an affine symmetric space
• Boundary value problem on symmetric homogeneous spaces
• Eigenfunctions of invariant differential operators on a symmetric space
• The orbits of affine symmetric spaces under the action of minimal parabolic subgroups
• A duality for symmetric spaces with applications to group representations
• Les espaces symétriques noncompacts