Multiple correlation sequences not approximable by nilsequences

Abstract

We show that there is a measure-preserving system $(X,\mathcal{B},\mu ,T)$ together with functions $F_0,F_1,F_2\in L^{\infty }(\mu )$ such that the correlation sequence $C_{F_0,F_1,F_2}(n)={\int }_X{F}_0\cdot T^n{F}_1\cdot T^{2n}{F}_{2}d\mu$ is not an approximate integral combination of $2$-step nilsequences.

14 pages

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• Gaussian width bounds with applications to arithmetic progressions in random settings

Cited by in corpus (1)

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