Fonctions généralisées sphériques sur $G_\mathbb{C}/G_\mathbb{R}$

DOI10.24033/asens.1597zbMath0714.43013OpenAlexW2598555140MaRDI QIDQ3200020

Pascale Harinck

Publication date: 1990

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1990_4_23_1_1_0

zbMATH Keywords

spherical functionsinvariant differential operatorssymmetric spacedifferential systemcompact Cartan subalgebraH-invariant generalized functionsemisimple complex group

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Spherical harmonics (33C55) Harmonic analysis and spherical functions (43A90)

Related Items (4)

Basis of the most continuous series of spherical generalized functions on \(G_C/G_R\) ⋮ Orbital functions on \(G_C/G_R\). Inversion formula of orbital integrals and Plancherel formula ⋮ Intégrales orbitales sur les groupes de Lie réductifs ⋮ 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 \(G_ \mathbb{C} /G_ \mathbb{R}\))

Cites Work

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• Invariant spherical distributions and the Fourier inversion formula on \(GL(n,{\mathbb{C}})/GL(n,{\mathbb{R}})\)
• Orbits on affine symmetric spaces under the action of the isotropy subgroups
• Discrete series for semisimple symmetric spaces
• Spherical generalized functions induced on \(G_{\mathbb{C}}/G_{\mathbb{R}}\) and applications
• Harmonic analysis on real reductive groups
• Kirillov's character formula for reductive Lie groups
• Discrete series for semisimple Lie groups. I: Construction of invariant eigendistributions
• Invariant eigendistributions on a semisimple Lie algebra
• Spherical Functions on a Semisimple Lie Group, I
• Les espaces symétriques noncompacts
• Invariant eigendistributions on semisimple Lie groups

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