Pointwise characteristic factors for the multiterm return times theorem

TL;DR

This paper extends previous work to identify pointwise characteristic factors for multidimensional return times averages, advancing understanding of nonconventional ergodic averages and their convergence properties.

Contribution

It proves that known L^2-characteristic factors are also pointwise characteristic for multidimensional return times averages, building on earlier results from 2003.

Findings

L^2-characteristic factors are pointwise characteristic for return times averages

Extension of previous results to multidimensional settings

Improved understanding of convergence in nonconventional ergodic averages

Abstract

This paper is an update and extension of a result the authors first proved in 2003. The goal of this paper is to study factors which are known to be L^2-characteristic for certain nonconventional averages and prove that these factors are pointwise characteristic for the multidimensional return times averages.