Harmonic analysis on reductive Lie groups (Q1159865)

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scientific article; zbMATH DE number 3745824

Language	Label	Description	Also known as
English	Harmonic analysis on reductive Lie groups	scientific article; zbMATH DE number 3745824

Statements

scholarly article

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Harmonic analysis on reductive Lie groups (English)

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D. P. Zhelobenko

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Journal of Soviet Mathematics

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publication date

1979

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zbMATH Keywords

reductive Lie group

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semisimple Lie group

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group representation

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character

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Plancherel measure

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Schwartz space

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Fourier transform

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spherical function

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MaRDI profile type

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Structure of representations generated by vectors of highest weight

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SPHERICAL FUNCTIONS ON HYPERBOLOIDS

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Holomorphic universal covering spaces of polynomials without multiple roots

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Atiyah-Patodi-Singer functionals for characteristic functionals for tangent bundles

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A property of the characters of irreducible representations of real semisimple Lie groups

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Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.

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Lie groups with square integrable representations

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Some tempered distributions on semi-simple groups of real rank one

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The Selberg trace formula for groups of F-rank one

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A theorem on the Schwartz space of a reductive Lie group

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The characters of discrete series as orbital integrals

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The spherical Bochner theorem on semisimple Lie groups

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Positive definite distributions on unimodular Lie groups

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Sur les représentations induites des groupes de Lie

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Zeta functions and their asymptotic expansions for compact locally symmetric spaces of negative curvature

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Singular Cauchy problems in symmetric spaces

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The restriction of admissible representations to \(n\)

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Sommes de Riesz et multiplicateurs sur un groupe de Lie compact

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Some applications of Grothendieck's theory of topological tensor products in harmonic analysis

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The Kunze-Stein phenomenon

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Quantization and Group Representations

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Limit formulas for multiplicities in \(L^2(\Gamma\setminus G)\)

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Harmonic analysis on the \(n\)-dimensional Lorentz group and its application to conformal quantum field theory

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Opérateurs différentiels bi-invariants sur un groupe de Lie

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The Fourier transform of the Schwartz space on a semisimple Lie group

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The Paley-Wiener theorem for distributions on symmetric spaces

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Some properties of the Fourier transform on semi-simple Lie groups. I

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Some Properties of the Fourier Transform on Semi-Simple Lie Groups. Part II

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Some Properties of the Fourier-Transform on Semisimple Lie Groups. III

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On the algebraic construction and classification of Harish-Chandra modules

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On an infinitesimal characterization of the discrete series

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The fundamental series of representations of a real semisimple Lie algebra

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Sur la racine carrée du noyau de Poisson dans les espaces symétriques et une conjecture de E. M. Stein

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Non-unitary dual spaces of groups

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Spherical functions are Fourier transforms of $L_1$-functions

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A Poisson formula for semi-simple Lie groups

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Translation-invariant cones of functions on semi-simple lie groups

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On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups

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On Selberg's trace formula

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Algebraically irreducible representations of \(L_1(G)\)

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A Theory of Spherical Functions. I

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Théorie des caractères. I. Algèbres unitaires. II. Définition et propriétés générales des caractéres

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Induced representations and finite volume homogeneous spaces

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Projective Limits in Harmonic Analysis

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Restriction to a parabolic subgroup and irreducibility of degenerate principal series of 𝑆𝑝(2,𝐶)

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The Dual of a Parabolic Subgroup and a Degenerate Principal Series of Sp(n, C)

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Plancherel Formula for Complex Semisimple Lie Groups

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The Plancherel Formula For Complex Semisimple Lie Groups

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Representations of a Semisimple Lie Group on a Banach Space. I

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Representations of semisimple Lie groups. II

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Representations of Semisimple Lie Groups IV

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Representations of Semisimple Lie Groups, V

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Representations of Semisimple Lie Groups VI: Integrable and Square-Integrable Representations

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ON THE PLANCHEREL FORMULA FOR THE RIGHT-INVARIANT FUNCTIONS ON A SEMISIMPLE LIE GROUP

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On the characters of a semisimple Lie group

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The Characters of Semisimple Lie Groups

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SPHERICAL FUNCTIONS ON A SEMISIMPLE LIE GROUP

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Differential Operators on a Semisimple Lie Algebra

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A Formula for Semisimple Lie Groups

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Spherical Functions on a Semisimple Lie Group, I

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Invariant eigendistributions on semisimple Lie groups

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Invariant Eigendistributions on a Semisimple Lie Group

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Discrete series for semisimple Lie groups. I: Construction of invariant eigendistributions

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Discrete series for semisimple Lie groups. II: Explicit determination of the characters

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Two theorems on semi-simple Lie groups

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Harmonic analysis on semisimple Lie groups

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Harmonic analysis on real reductive groups. I: The theory of the constant term

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Harmonic analysis on real reductive groups. II: Wave-packets in the Schwartz space

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Harmonic analysis on real reductive groups. III: The Maass-Selberg relations and the plancherel formula

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The characters of representations of Harish-Chandra

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A proof of Blattner's conjecture

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Differential operators on homogeneous spaces

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Duality and Radon Transform for Symmetric Spaces

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Radon-Fourier transforms on symmetric spaces and related group representations

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The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds

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An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces

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Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces

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A duality for symmetric spaces with applications to group representations

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The surjectivity of invariant differential operators on symmetric spaces. I

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A duality for symmetric spaces with applications to group representations. II: Differential equations and eigenspace representations

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Invariant differential equations on homogeneous manifolds

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Some results on eigenfunctions on symmetric spaces and eigenspace representations.

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The bounded spherical functions on symmetric spaces

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A Fatou-type theorem for harmonic functions on symmetric spaces

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Character formulas for discrete series on semisimple Lie groups

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A uniqueness theorem for tempered invariant eigendistributions

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Singular invariant eigendistributions as characters

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Some remarks on invariant eigendistributions on semisimple Lie groups

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Supplements and corrections to my paper: The characters of some induced representations of semisimple Lie groups

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Eigenfunctions of the Laplacian on a real hyperboloid of one sheet

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Multiplicity formulae for discrete series

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Functional analysis on SU(1,1)

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Differential equations and an analog of the Paley-Wiener theorem for linear semisimple Lie groups

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Composition Series and Intertwining Operators for the Spherical Principal Series. II

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Composition Series and Intertwining Operators for the Spherical Principal Series. I

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On the annihilators of the simple subquotients of the principal series

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Eigenfunctions of invariant differential operators on a symmetric space

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Harmonic functions on real hyperbolic spaces

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The Plancherel formula for parabolic subgroups

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Fatou's theorem for symmetric spaces. I

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Weyl group of a cuspidal parabolic

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Intertwining operators for semisimple groups

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Singular Integrals and the Principal Series, IV

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Szegoe kernels associated with discrete series

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Classification of irreducible tempered representations of semisimple Lie groups

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Boundary Behavior of Poisson Integrals on Symmetric Spaces

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Realization of Hermitian symmetric spaces as generalized half-planes

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On convexity, the Weyl group and the Iwasawa decomposition

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On the tensor product of a finite and an infinite dimensional representation

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On Representations of the Group SU(n, 1)

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Uniformly Bounded Representations, II. Analytic Continuation of the Principal Series of Representations of the n x n Complex Unimodular Group

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Uniformly Bounded Representations III: Intertwining Operators for the Principal Series on Semisimple Groups

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The Dimension of Spaces of Automorphic Forms

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Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif

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Algebraic Results on Representations of Semisimple Lie Groups

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Multiplicity formulas for certain semisimple Lie groups

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On the Harish-Chandra Homomorphism

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Conical Vectors in Induced Modules

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Existence of conical vectors in induced modules

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On the Uniqueness of Conical Vectors

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Uniqueness of Embeddings of Certain Induced Modules

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Generalized Verma modules, the Cartan-Helgason theorem, and the Harish- Chandra homomorphism

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A generalization of the Bernstein-Gelfand-Gelfand resolution

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Minimal K-types for certain representations of real semisimple groups

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Fatou's theorem for symmetric spaces

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Potential theory in bounded symmetric homogeneous complex domains

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On Blattner's formula for the discrete series representations of \(SO(2n,1)\)

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The horospheric approach to harmonic analysis on a semi-simple Lie group

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The characters of the holomorphic discrete series

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Square integrable representations and the Fourier algebra of a unimodular group

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Fourier Analysis and Symmetric Spaces

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Eigenfunctions of the Laplacian on a Hermitian hyperbolic space

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An analogue of the Borel-Weil-Bott theorem for Hermitian symmetric pairs of non-compact type

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The Paley-Wiener tpye theorem for finite covering groups of SU(1,1)

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Boundary value problem on symmetric homogeneous spaces

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An algebraic construction of a class of representations of a semi-simple Lie algebra

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Representations of complex semisimple Lie groups and Lie algebras

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Representation of complex semi-simple Lie groups and Lie algebras

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Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups

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Decomposition of C ∞ Intertwining Operators for Lie Groups

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A Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical Functions on a Semisimple Lie Group

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A convolution integral for Fourier transforms on the group \(\text{SL}(2, \mathbb C)\)

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An elementary proof of the Plancherel theorem for the classical groups

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Intégrales d'entrelacement et fonctions de Whittaker

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On the characters of the discrete series. The Hermitian symmetric case

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Some properties of squareintegrable representations of semisimple Lie groups

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\(L^2\)-cohomology and the discrete series

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Heisenberg subgroups of semisimple Lie groups

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Positive operators and automorphism groups of bounded symmetric domains

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Fourier analysis on compact symmetric space

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Conjugate classes of Cartan subalgebras in real semisimple Lie algebras

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Positive definite distributions on \(K\setminus G/K\)

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Convergence of Fourier series on compact Lie groups

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Analysis in matrix spaces and some new representations of \(SL(N,\mathbb{C})\)

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Analytic continuation of group representations

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A Sufficient Condition for an Integral Operator to Have a Trace.

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Integrability of Fourier transforms for unimodular Lie groups

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Harmonic analysis on hyperboloids

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Direct integral theory for weights, and the Plancherel formula

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Sur les représentations unitaires des groupes de Lorentz généralisés

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Le théorème de Paley-Wiener pour l'espace des fonctions indefiniment différentiable et à support compact sur un espace symétrique de type non-compact

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Spherical transforms on semisimple Lie groups

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On the representations of $SL \left( {3, C} \right)$, I

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The Plancherel transform on SL//2(k) and its application to the decomposition of tensor products of irreducible representations

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Unitary representations of $SL \left( {n,C} \right)$

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Analytic continuation of the holomorphic discrete series of a semi-simple Lie group

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Structure of certain induced representations of complex semisimple Lie algebras

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On $L_p$ Fourier multipliers on certain symmetric spaces.

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Cyclic Vectors and Irreducibility for Principal Series Representations

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Cyclic Vectors and Irreducibility for Principal Series Representations. II

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On Harish-Chandra's Generalized C-Functions

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On the Selberg trace formula in the case of compact quotient

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An asymptotic formula of Gelfand and Gangolli for the spectrum of \(\Gamma\setminus G\)

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On the Enright-Varadarajan modules : a construction of the discrete series

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The Dual Space of Semi-Simple Lie Groups

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Homogeneous Spaces with Finite Invariant Measure

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On the Weyl coefficients of SO(<i>n</i>)

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Invariant means and ergodic sets in Fourier analysis

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Tensor products of finite and infinite dimensional representations of semisimple Lie groups

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Identifiers

zbMATH Open document ID

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10.1007/BF01375564

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1159865

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