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A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems
Published online by Cambridge University Press: 07 September 2017
Abstract
We investigate how spectral properties of a measure-preserving system $(X,{\mathcal{B}},\unicode[STIX]{x1D707},T)$ are reflected in the multiple ergodic averages arising from that system. For certain sequences $a:\mathbb{N}\rightarrow \mathbb{N}$, we provide natural conditions on the spectrum $\unicode[STIX]{x1D70E}(T)$ such that, for all $f_{1},\ldots ,f_{k}\in L^{\infty }$,
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- © Cambridge University Press, 2017
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