Van der Corput's difference theorem for amenable groups and the left regular representation
Abstract
We establish a connection between two variants of van der Corput's Difference Theorem (vdCDT) for countably infinite amenable groups and the ergodic hierarchy of mixing properties of a unitary representation of . In particular, we show that one variant of vdCDT corresponds to subrepresentations of the left regular representation, and another variant of vdCDT corresponds to the absence of finite dimensional subrepresentations. We then obtain applications for measure preserving actions of countably infinite abelian groups.
Cite
@article{arxiv.2308.05560,
title = {Van der Corput's difference theorem for amenable groups and the left regular representation},
author = {Sohail Farhangi},
journal= {arXiv preprint arXiv:2308.05560},
year = {2024}
}
Comments
26 pages. This third edition is the journal edition. More referee comments have been incorporated, and the generality has been reduced from locally compact second countable amenable groups to countably infinite amenable groups