Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groups

TL;DR

This paper establishes a mean ergodic theorem for amenable discrete quantum groups and applies it to prove a Wiener type theorem for measures on compact metrizable groups, advancing the understanding of quantum and classical harmonic analysis.

Contribution

The paper introduces a mean ergodic theorem for amenable discrete quantum groups and extends it to a Wiener type theorem for measures on compact metrizable groups, bridging quantum and classical analysis.

Findings

Proved a mean ergodic theorem for amenable discrete quantum groups.

Established a Wiener type theorem for continuous measures on compact metrizable groups.

Connected quantum group ergodic theory with classical harmonic analysis results.

Abstract

We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.