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Convergence of Conze–Lesigne averages

  • BERNARD HOST (a1) and BRYNA KRA (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385701001249
  • Published online: 01 March 2001
Abstract

We study the convergence of N^{-1} \sum f_1(T^{a_1n}x)f_2(T^{a_2n}x)f_3(T^{a_3n}x), for a measure-preserving system (X, \mathcal{B}, \mu, T) and f_{1}, f_{2}, f_{3} \in L^{\infty}(\mu). This generalizes the theorem of Conze and Lesigne on such expressions and simplifies the proof. We also obtain a description of the limit.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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