engleski

Ergodic characterization of van der Corput sets

We prove an analogue to the well known equivalence of intersective sets and Poincare-recurrent sets, in a stronger setting. We show that a set D is van der Corput, if and only if for each Hilbert space H, unitary operator U, and $x\in H$ such that the projection of x to the kernel of (U-I) is nonvanishing, there exists $d\in D$, such that $(U^{; ; ; d}; ; ; x, x)\not=0$.

Van der Corput sets; recurrence; intersectivity; correlativity; Furstenberg correspondence principle

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