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Integer part polynomial correlation sequences

Published online by Cambridge University Press:  19 September 2016

ANDREAS KOUTSOGIANNIS*
Affiliation:
The Ohio State University, Department of Mathematics, Columbus, OH, USA email koutsogiannis.1@osu.edu

Abstract

Following an approach presented by Frantzikinakis [Multiple correlation sequences and nilsequences. Invent. Math. 202(2) (2015), 875–892], we prove that any multiple correlation sequence defined by invertible measure preserving actions of commuting transformations with integer part polynomial iterates is the sum of a nilsequence and an error term, which is small in uniform density. As an intermediate result, we show that multiple ergodic averages with iterates given by the integer part of real-valued polynomials converge in the mean. Also, we show that under certain assumptions the limit is zero. A transference principle, communicated to us by M. Wierdl, plays an important role in our arguments by allowing us to deduce results for $\mathbb{Z}$-actions from results for flows.

Type
Original Article
Copyright
© Cambridge University Press, 2016 

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