Convergence of multiple ergodic averages for some commuting transformations

Nikos Frantzikinakis; Bryna Kra

doi:10.1017/S0143385704000616

Convergence of multiple ergodic averages for some commuting transformations

Nikos Frantzikinakis^*, Bryna Kra

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-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 7_i and each pair 7_iT _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 language	English (US)
Pages (from-to)	799-809
Number of pages	11
Journal	Ergodic Theory and Dynamical Systems
Volume	25
Issue number	3
DOIs	https://doi.org/10.1017/S0143385704000616
State	Published - Jun 2005

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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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.",

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