Conditions for rational weak mixing

TL;DR

This paper explores the properties of measure-preserving transformations, identifying conditions under which certain weak mixing behaviors occur and providing criteria for the smoothness of renewal sequences.

Contribution

It introduces new examples of rationally ergodic, weakly mixing transformations that lack subsequence rational weak mixing and establishes a condition for renewal sequence smoothness.

Findings

Existence of rationally ergodic, weakly mixing transformations not subsequence rationally weakly mixing

A new condition for the smoothness of renewal sequences

Insights into the structure of measure-preserving transformations

Abstract

We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.