Convergence of multiple ergodic averages for some commuting transformations

Nikos Frantzikinakis*, Bryna Kra

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We prove the L2-convergence for the linear multiple ergodic averages of commuting transformations T1,..., T2), assuming that each map 7i and each pair 7iT j-1 is ergodic for i ≠ j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.

Original languageEnglish (US)
Pages (from-to)799-809
Number of pages11
JournalErgodic Theory and Dynamical Systems
Volume25
Issue number3
DOIs
StatePublished - Jun 2005

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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