Orbital functions on \(G_C/G_R\). Inversion formula of orbital integrals and Plancherel formula

DOI10.1006/jfan.1997.3163zbMath0899.22015OpenAlexW2005547055MaRDI QIDQ1381580

Pascale Harinck

Publication date: 18 March 1998

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

Full work available at URL: https://doi.org/10.1006/jfan.1997.3163

zbMATH Keywords

inversion formulaPlancherel formuladifferential operatorssymmetric spacesemisimple Lie groupreal formspherical generalized functionsorbital functions

Mathematics Subject Classification ID

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

Related Items (3)

Invariant fundamental solutions and solvability for symmetric spaces of type \( G_C / G_ R \) with only one conjugacy class of Cartan subspaces ⋮ The Plancherel decomposition for a reductive symmetric space. I: Spherical functions ⋮ Équations différentielles invariantes sur les groupes et algèbres de Lie réductifs. (Invariant differential equations on reductive Lie groups and Lie algebras)

Cites Work

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• Sur les caractères des groupes de Lie réductifs non connexes. (On the characters of non-connected reductive Lie groups)
• Coefficients généralisés de séries principales sphériques et distributions sphériques sur \(G_ \mathbb{C} /G_ \mathbb{R}\). (Generalized coefficients of spherical principal series and spherical distributions over \(G_ \mathbb{C} /G_ \mathbb{R}\))
• Distributions sphériques invariantes sur les espaces symétriques semi-simples \(G_ c/G\). (Invariant spherical distributions over the semi-simple symmetric spaces \(G_ c/G\))
• Spherical generalized functions induced on \(G_{\mathbb{C}}/G_{\mathbb{R}}\) and applications
• Harmonic analysis on real reductive groups
• Orbital integrals on reductive Lie algebras
• Correspondence of spherical distributions between two symmetric spaces of type \(G_ C/G_ R\)
• Basis of the most continuous series of spherical generalized functions on \(G_C/G_R\)
• Inversion formula of orbital integrals on reductive Lie groups
• Fonctions généralisées sphériques sur $G_\mathbb{C}/G_\mathbb{R}$
• Intégrales orbitales sur les groupes de Lie réductifs

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