No representation of Moore groups and affine groups has any rate of random mixing

2005/02/16 by C. R. E. Raja, Raja, C. R. E.
Mathematics · #22D10 #37A25 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Limits and Structures in Graph Theory #math.DS #msc:22D10 #msc:37A25

paper · pdf · doi:10.48550/arxiv.math/0502343

7 pages

arxiv created 2005/02/16 · openalex publication_date 2005/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A sequence a_n\da 0 forms a rate of random mixing for a unitary system (G,μ, π, \cal H) if for any u, v∈ \cal H \limsup ||\over a_n lt; ∞ a.e. ω in the probability space (G^{\mathbb N}, μ^{\mathbb N}) of the random walk induced by μ. We study the class of locally compact groups none of whose representation has any rate of random mixing and prove that this class contains Moore groups and certain solvable groups which includes the group of affine transformations on a local field.

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