Norm convergence of nilpotent ergodic averages

TL;DR

This paper proves that multiple polynomial ergodic averages associated with nilpotent groups of measure-preserving transformations always converge in the L^2 norm, advancing understanding of ergodic behavior in such systems.

Contribution

It establishes the norm convergence of polynomial ergodic averages for nilpotent groups, a significant extension of previous convergence results.

Findings

Proved L^2 norm convergence for nilpotent polynomial ergodic averages.

Extended ergodic theorems to a broader class of group actions.

Provided new tools for analyzing polynomial averages in ergodic theory.

Abstract

We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L^2 norm.