Convergence of polynomial ergodic averages

Bernard Host; Bryna Kra

doi:10.1007/BF02772534

Convergence of polynomial ergodic averages

Bernard Host^*, Bryna Kra

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

57 Scopus citations

Abstract

We prove the L² convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.

Original language	English (US)
Pages (from-to)	1-19
Number of pages	19
Journal	Israel Journal of Mathematics
Volume	149
DOIs	https://doi.org/10.1007/BF02772534
State	Published - 2005

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF02772534

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title = "Convergence of polynomial ergodic averages",

abstract = "We prove the L2 convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.",

author = "Bernard Host and Bryna Kra",

note = "Funding Information: * The second author was partially supported by NSF grant DMS-0244994. Received June 5, 2003 and in revised form October 9, 2003",

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volume = "149",

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N2 - We prove the L2 convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.

AB - We prove the L2 convergence for an ergodic average of a product of functions evaluated along polynomial times in a totally ergodic system. For each set of polynomials, we show that there is a particular factor, which is an inverse limit of nilsystems, that controls the limit behavior of the average. For a general system, we prove the convergence for certain families of polynomials.

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