Spherical functions and harmonic analysis on free groups

DOI10.1016/0022-1236(82)90108-2zbMath0489.43008OpenAlexW1976041553MaRDI QIDQ1166746

Massimo A. Picardello, Alessandro Figà-Talamanca

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0022-1236(82)90108-2

zbMATH Keywords

Plancherel measurefree groupcomplementary seriesspherical functionradial functionsprincipal seriesirreducible unitary representation

Mathematics Subject Classification ID

Unitary representations of locally compact groups (22D10) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Harmonic analysis and spherical functions (43A90)

Related Items

Equivalence of two series of spherical representations of a free group, A theorem of Roe and Strichartz on homogeneous trees, Free group representations: Duplicity and oddity on the boundary, Bergman spaces and Carleson measures on homogeneous isotropic trees, Universal properties of the isotropic Laplace operator on homogeneous trees, Harmonic analysis on the free product of two cyclic groups, An analytic series of irreducible representations of the free group, Proper isometric actions of hyperbolic groups on -spaces, The extension problem in free harmonic analysis, An inversion formula for the Radon transform on trees, Free group representations from vector-valued multiplicative functions. II, Spherical functions and local limit theorems on free groups, A characterization of weak \(L^p\)-eigenfunctions of the Laplacian on homogeneous trees, Analyse harmonique des groupes d'automorphismes d'arbres de Bruhat-Tits, Characterization of positive definite, radial functions on free groups, $L^p$-boundedness of pseudo-differential operators on homogeneous trees, Groups of hierarchomorphisms of trees and related Hilbert spaces, Dynamics of semigroups generated by analytic functions of the Laplacian on homogeneous trees, Spectral measures of factor of i.i.d. processes on vertex-transitive graphs, Stability properties of multiplicative representations of the free group, Convergence of Fourier Series Expansion Related to Free Groups, A Characterization of Spherical Series Representations of the Free Group, Size of matrix coefficients characterizes anisotropic principal series representations of the free group, Free group representations from vector-valued multiplicative functions. I, A Lévy-Khinchin formula for free groups, SCHUR MULTIPLIERS AND SPHERICAL FUNCTIONS ON HOMOGENEOUS TREES, Carleson measures for non-negative subharmonic functions on homogeneous trees, Restrictions of the special representation of \(\text{Aut}(\text{tree}_ 3)\) to two cocompact subgroups, An analytic family of uniformly bounded representations of free groups, Représentations sphériques des groupes agissant transitivement sur un arbre semi-homogène, Poisson transform on a locally finite tree, The Poisson transform and representations of a free group, The Plancherel measure for polygonal graphs, Cogrowth of groups and simple random walks, Norms of Free Operators, The Plancherel measure for symmetric graphs, Drifted Laplace operators on homogeneous trees, Probability measures on groups and some related ideals in group algebras

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