A van der Corput lemma and weak mixing over groups

2005/12/02 by Conrad Beyers, Beyers, Conrad, Rocco Duvenhage +4 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.math/0512059

31 pages

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

Abstract

We study weak mixing of all orders for weakly mixing measure preserving dynamical systems, where the dynamics is given by the action of an abelian second countable topological group which has an invariant measure under the group operation. One of the main technical tools we use is a van der Corput lemma for Hilbert space valued functions on a second countable topological group.

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