Formules limites et formules asymptotiques pour les multiplicités dans \(L^ 2(G/\Gamma)\). (Limit formulas and asymptotic formulas for the multiplicities in \(L^ 2(G/\Gamma))\)

DOI10.1215/S0012-7094-86-05338-XzbMath0623.22012MaRDI QIDQ1091487

Patrick Delorme

Publication date: 1986

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Plancherel measureSelberg trace formulasemisimple Lie groupdiscrete seriesregular representationspherical principal seriesdiscrete cocompact torsion free subgrouplimit formulainvariant Paley-Wiener theorem\(L^ 2(G/\Gamma )\)p- Schwartz space

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Discrete subgroups of Lie groups (22E40) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (15)

Méthode des orbites pour les représentations de longueur finie. II ⋮ Continuity of the Mackey-Higson bijection ⋮ An approximation principle for congruence subgroups. II: Application to the limit multiplicity problem ⋮ Analytic torsion of arithmetic quotients of the symmetric space \(\mathrm{SL} (n,\mathbb{R})/ \mathrm{SO}(n)\) ⋮ Asymptotics of Automorphic Spectra and the Trace Formula ⋮ Relative trace formulae and the Gan-Gross-Prasad conjectures ⋮ Linear intertwining periods and epsilon dichotomy for linear models ⋮ On the Arthur-Selberg trace formula for \(\mathrm{GL}(2)\) ⋮ Towards a Paley-Wiener theorem for semisimple symmetric spaces ⋮ Limit formulas of period integrals for a certain symmetric pair ⋮ Limit formulas of period integrals for a certain symmetric pair. II ⋮ Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds ⋮ Sur les groupes $EXT^n$ des représentations des groupes de Lie semi-simples ⋮ Limit multiplicities for \({\text{SL}}_2(\mathcal{O}_F)\) in \({\text{SL}}_2(\mathbb{R}^{r_1}\oplus\mathbb{C}^{R_2})\) ⋮ LIMIT MULTIPLICITIES FOR PRINCIPAL CONGRUENCE SUBGROUPS OF AND

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multipliers for the convolution algebra of left and right K-finite compactly supported smooth functions on a semi-simple Lie group
• A Paley-Wiener theorem for real reductive groups
• Classification of irreducible tempered representations of semisimple groups. I
• Théoreme de type Paley-Wiener pour les groupes de Lie semi-simples réels avec une seule classe de conjugaison de sous groupes de Cartan
• Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. (The invariant Paley-Wiener theorem for reductive Lie groups)
• The algebraic structure of the representation of semisimple Lie groups. I
• Spectra of compact locally symmetric manifolds of negative curvature
• Intertwining operators for semisimple groups. II
• Reducibility of generalized principal series representations
• Discrete series for semisimple symmetric spaces
• Representations of real reductive Lie groups
• Limit formulas for multiplicities in \(L^ 2(\Gamma-G)\). II: The tempered spectrum
• On Selberg's trace formula
• Harmonic analysis on real reductive groups. III: The Maass-Selberg relations and the plancherel formula
• The Plancherel measure in nilpotent Lie groups as a limit of point measures
• Limit formulas for multiplicities in \(L^2(\Gamma\setminus G)\)
• Asymptotic behaviour of matrix coefficients of the discrete series
• The Dual Spaces of C ∗ -Algebras
• Some results on invariant theory
• Homomorphismes de Harish-Chandra liés aux $K$-types minimaux des séries principales généralisées des groupes de Lie réductifs connexes
• The Minakshisundaram-Pleijel Coefficients for the Vector Valued Heat Kernel on Compact Locally Symmetric Spaces of Negative Curvature
• Weyl group of a cuspidal parabolic
• The Dual Topology for the Principal and Discrete Series on Semisimple Groups
• Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. II

This page was built for publication: Formules limites et formules asymptotiques pour les multiplicités dans \(L^ 2(G/\Gamma)\). (Limit formulas and asymptotic formulas for the multiplicities in \(L^ 2(G/\Gamma))\)