The principal series for a reductive symmetric space. II: Eisenstein integrals

DOI10.1016/0022-1236(92)90021-AzbMath0791.22008OpenAlexW2162784751MaRDI QIDQ1803326

Erik P. van den Ban

Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90021-a

zbMATH Keywords

Fourier transformparabolic subgroupsPlancherel formulairreducible unitary representationsSchwartz functions\(c\)-functionprincipal series representationsreductive symmetric spaceEisenstein integralstempered representationsCartan involution

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46)

Related Items (30)

Volume growth, temperedness and integrability of matrix coefficients on a real spherical space ⋮ Expansions for Eisenstein integrals on semisimple symmetric spaces ⋮ The principal series for a reductive symmetric space. I. $H$-fixed distribution vectors ⋮ Schwartz space for the hypergeometric Fourier transform. (With an appendix by Mustapha Tinfou) ⋮ The action of intertwining operators on spherical vectors in the minimal principal series of a reductive symmetric space ⋮ Eisenstein series on weakly spherical homogeneous spaces of \(GL(n)\) ⋮ Cusp forms for reductive symmetric spaces of split rank one ⋮ Truncation for reductive symmetric spaces ⋮ Unnamed Item ⋮ Radon transformation on reductive symmetric spaces: support theorems ⋮ Symmetric subvarieties in compactifications and the Radon transform on Riemannian symmetric spaces of noncompact type. ⋮ Decay of matrix coefficients on reductive homogeneous spaces of spherical type ⋮ Normalizations of Eisenstein integrals for reductive symmetric spaces ⋮ Poisson transforms on vector bundles ⋮ Plancherel theory for real spherical spaces: Construction of the Bernstein morphisms ⋮ Paley-Wiener theorems for hyperbolic spaces ⋮ The notion of cusp forms for a class of reductive symmetric spaces of split rank 1 ⋮ Cuspidal discrete series for semisimple symmetric spaces ⋮ Embeddings of discrete series for a reductive symmetric space ⋮ Filtration of certain spaces of functions on a reductive symmetric space ⋮ Support of asymptotics and growth of eigenfunctions on a semisimple symmetric space ⋮ ``Generalized Schur orthogonality relations for reductive symmetric spaces ⋮ The Schwartz algebra of an affine Hecke algebra ⋮ Cuspidal integrals for \(\mathrm{SL}(3) / K_\epsilon\) ⋮ The Radon transform for double fibrations of semisimple symmetric spaces ⋮ Fourier inversion on a reductive symmetric space ⋮ The Plancherel decomposition for a reductive symmetric space. I: Spherical functions ⋮ The Plancherel decomposition for a reductive symmetric space. II: Representation theory ⋮ A generalised Gangolli-Lévy-Khintchine formula for infinitely divisible measures and Lévy processes on semi-simple Lie groups and symmetric spaces ⋮ Fonctions \(\mathbb {D}\)(G/H)-finies sur un espace symétrique réductif. (\(\mathbb {D}\)(G/H)-finite functions on a reductive symmetric space)

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