Harmonic functions on compactly generated groups

DOI10.1142/S0129167X22500264MaRDI QIDQ5068527

Darren Creutz

Publication date: 6 April 2022

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.07948

zbMATH Keywords

topological groupcohomologyunitary representationharmonic functionintegrationprobability measureproperty Tharmonic cocycle

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Measures on groups and semigroups, etc. (43A05) Unitary representations of locally compact groups (22D10) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) General properties and structure of locally compact groups (22D05) Induced representations for locally compact groups (22D30) Summability methods on groups, semigroups, etc. (43A55)

Cites Work

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• Characterisations of algebraic properties of groups in terms of harmonic functions
• Factor and normal subgroup theorems for lattices in products of groups
• Random walks on discrete groups: Boundary and entropy
• Harmonic forms with values in locally constant Hilbert bundles
• Finite-dimensional representations constructed from random walks
• Harmonic cocycles, von Neumann algebras, and irreducible affine isometric actions
• A Poisson formula for semi-simple Lie groups
• A new proof of Gromov’s theorem on groups of polynomial growth
• A functional analysis proof of Gromov's polynomial growth theorem

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