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arXiv · 2412.17409

Discrete spectrum of probability measures for locally compact group actions

Zongrui Hu·Xiao Ma·Leiye Xu·Xiaomin Zhou
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Abstract

In this paper, we investigate the discrete spectrum of probability measures for actions of locally compact groups. We establish that a probability measure has a discrete spectrum if and only if it has bounded measure-max-mean-complexity. As applications: 1) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it has bounded mean-complexity along F\o lner sequences; 2) An invariant measure for a locally compact amenable group action has a discrete spectrum if and only if it is mean equicontinuous along a tempered F\o lner sequence, or equicontinuous in the mean along a tempered F\o lner sequence.

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Zongrui Hu, Xiao Ma, Leiye Xu, Xiaomin Zhou. 2024-12-23. Discrete spectrum of probability measures for locally compact group actions. https://arxiv.org/abs/2412.17409

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