Transition operators on co-compact \(G\)-spaces
type: Item
instance of: scholarly article
title: Transition operators on co-compact \(G\)-spaces
zbMATH Open document ID: 1116.22007
DOI: 10.4171/RMI/473
author: Wolfgang Woess
author: Laurent Saloff-Coste
published in: Revista Matemática Iberoamericana
publication date: 2007-05-03T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1169480030
full work available at URL: https://eudml.org/doc/41991
review text: The authors prove the following result: Let \(M\) be a complete, co-compact Riemannian manifold. Then \(0\) is in the \(L^2\)-spectrum of the Laplacian of \(M\) if and only if some (equivalently, every) closed quasi-transitive group of isometries of \(M\) is both amenable and unimodular. The same result holds also for Euclidean simplicial complexes.
Mathematics Subject Classification ID: 22F50
Mathematics Subject Classification ID: 43A07
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 58C40
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 5149118
zbMATH Keywords: \(G\)-space
zbMATH Keywords: proper action
zbMATH Keywords: isometries
zbMATH Keywords: invariant transition operator
zbMATH Keywords: amenability
reviewed by: Mircea Puta
MaRDI profile type: Publication
cites work: On the relation between amenability of locally compact groups and the norms of convolution operators
cites work: Sur la norme des opérateurs de convolution
cites work: Brownian motion, harmonic functions and hyperbolicity for Euclidean complexes
cites work: The fundamental group and the spectrum of the Laplacian
cites work: Random walks on the affine group of local fields and of homogeneous trees
cites work: The spectrum of the continuous Laplacian on a graph
cites work: Connected Lie groups and property RD
cites work: Q5566981
cites work: Q4213399
cites work: Non-Gaussian Aspects of Heat Kernel Behaviour
cites work: Convolutions, means, and spectra
cites work: Q4086511
cites work: Q5180138
cites work: Transformation groups
cites work: Harmonic maps between Riemannian polyhedra. With a preface by M. Gromov
cites work: A rigidity theorem for the solvable Baumslag-Solitar groups. (With an appendix by Daryl Cooper)
cites work: Croissance polynomiale et périodes des fonctions harmoniques
cites work: Q3894703
cites work: Q5596533
cites work: The Theory of p-Spaces with an Application to Convolution Operators
cites work: Q5723435
cites work: Full Banach Mean Values on Countable groups.
cites work: Periodic Schrödinger Operators on a Manifold
cites work: Estimations \(L^ p\) des coefficients de représentation et opérateurs de convolution
cites work: General Irreducible Markov Chains and Non-Negative Operators
cites work: Q5533878
cites work: The isoperimetric profile of homogeneous Riemannian manifolds.
cites work: Q5669004
cites work: Q4520727
cites work: Q5516901
cites work: Aspects of Sobolev-type inequalities
cites work: Computing Norms of Group-Invariant Transition Operators
cites work: Transition operators, groups, norms, and spectral radii
cites work: On the norms of group-invariant transition operators on graphs
cites work: Q4049667
cites work: Non-negative matrices and Markov chains. 2nd ed
cites work: Amenability, unimodularity, and the spectral radius of random walks on infinite graphs
cites work: Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
cites work: Discrete Schrödinger operators on a graph
cites work: Q3482602
cites work: Q3959179
cites work: A generalized Følner condition and the norms of random walk operators on groups
OpenAlex ID: W1972415491
description: scientific article; zbMATH DE number 5149118