Multiple correlation sequences not approximable by nilsequences
Ergodic Theory and Dynamical Systems p. 1- 12
We show that there is a measure-preserving system (X,B,μ,T) together with functions F0,F1,F2∈L∞(μ) such that the correlation sequence CF0,F1,F2(n)=∫XF0⋅TnF1⋅T2nF2dμ is not an approximate integral combination of 2-step nilsequences.
|Ergodic Theory and Dynamical Systems|
|Organisation||Centrum Wiskunde & Informatica, Amsterdam, The Netherlands|
Briët, J, & Green, B. (2021). Multiple correlation sequences not approximable by nilsequences. Ergodic Theory and Dynamical Systems, 1–12. doi:10.1017/etds.2021.66