Decomposition of multicorrelation sequences and joint ergodicity

2021/06/02 by Donoso, Sebastián, Moragues, Andreu Ferré, Koutsogiannis, Andreas +1 · 1 citation
#28A99 (Secondary) #37A05 (Primary) 37A30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.01058

Abstract

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving ℤ^d-actions with multivariable integer polynomial iterates is the sum of a nilsequence and a null sequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on ℤ^d-systems.

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