Spherical distributions on the pseudo-Riemannian space SL(n, \({\mathbb{R}})/GL(n-1,\,{\mathbb{R}})\)

DOI10.1016/0022-1236(86)90004-2zbMath0607.43008OpenAlexW1997580939MaRDI QIDQ1085382

M. T. Kosters, Gerrit Van Dijk

Publication date: 1986

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(86)90004-2

zbMATH Keywords

asymptoticsPlancherel formulaspherical distributionsconnected semisimple Lie groupprincipal nonunitary series of representationspseudo- Riemannian symmetric space

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46) Harmonic analysis and spherical functions (43A90)

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A new class of Gelfand pairs, Spherical distributions on the pseudo-Riemannian space SL(n, \({\mathbb{R}})/GL(n-1,\,{\mathbb{R}})\), The Plancherel formula for the line bundles on \(\mathrm{SL}(n + 1, \mathbb{R})/S(\mathrm{GL}(1,\mathbb{R})\times \mathrm{GL}(n, \mathbb{R}))\), Invariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one, Projective pseudodifferential analysis and harmonic analysis, Orbital integrals on Lorentzian symmetric spaces, The notion of cusp forms for a class of reductive symmetric spaces of split rank 1, Distributions coniques sur le cône des matrices de rang un et de trace nulle, Unnamed Item, Eigenspaces of the Laplacian on hyperbolic spaces: composition series and integral transforms, \((\mathrm{GL}(n+1,\mathbb R),\mathrm{GL}(n,\mathbb R))\) is a generalized Gelfand pair, Unnamed Item

Cites Work

• Spherical distributions on the pseudo-Riemannian space SL(n, \({\mathbb{R}})/GL(n-1,\,{\mathbb{R}})\)
• Spherical functions on a real semisimple Lie group. A method of reduction to the complex case
• Eigenspaces of invariant differential operators on an affine symmetric space
• Distributions spheriques sur les espaces hyperboliques
• Discrete series for semisimple symmetric spaces
• Harmonic analysis on real reductive groups
• Distributions Invariant under an Orthogonal Group of Arbitrary Signature.
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