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Archiv der Mathematik

, Volume 98, Issue 4, pp 355–360 | Cite as

Ergodic characterization of van der Corput sets

  • Marina Ninčević
  • Braslav Rabar
  • Siniša Slijepčević
Article

Abstract

We prove an analogue to the well-known equivalence of intersective sets and Poincaré 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 (UI) is nonvanishing, there exists \({d \in D\,}\) such that (U d x, x)≠ 0. We also characterize the smallest such d.

Mathematics Subject Classification

37A45 11P99 37B20 

Keywords

Van der Corput sets Recurrence Intersectivity Correlativity Furstenberg correspondence principle 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Marina Ninčević
    • 1
  • Braslav Rabar
    • 1
  • Siniša Slijepčević
    • 1
  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia

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