Return times theorem for amenable groups

TL;DR

This paper generalizes Bourgain's return times theorem from classical settings to all locally compact second countable amenable groups, broadening its applicability in ergodic theory.

Contribution

It extends the return times theorem to a wider class of groups using an orthogonality criterion, providing a new theoretical framework.

Findings

Extended the return times theorem to all locally compact second countable amenable groups

Developed a version of the orthogonality criterion for these groups

Provided a new proof technique based on orthogonality for the theorem

Abstract

We extend Bourgain's return times theorem to arbitrary locally compact second countable amenable groups. The proof is based on a version of the Bourgain--Furstenberg--Katznelson--Ornstein orthogonality criterion.