Rigidity Sequences of Power Rationally Weakly Mixing Transformations

TL;DR

This paper demonstrates that a specific class of infinite measure preserving transformations with strong weak mixing properties can generate all possible rigidity sequences of conservative ergodic invertible measure preserving transformations on Lebesgue measure spaces.

Contribution

It establishes a comprehensive link between a class of transformations and the rigidity sequences of all conservative ergodic measure preserving transformations.

Findings

Class of transformations generates all rigidity sequences.

Strong weak mixing condition is sufficient.

Universal property for rigidity sequences.

Abstract

We prove that a class of infinite measure preserving transformations, satisfying a "strong" weak mixing condition, generates all rigidity sequences of all conservative ergodic invertible measure preserving transformations defined on a Lebesgue $\sigma$-finite measure space.