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Ergodic averages with deterministic weights

Fabien Durand, Dominique Schneider (2002)

Annales de l’institut Fourier

We study the convergence of the ergodic averages 1 N k = 0 N - 1 θ ( k ) f T u k where ( θ ( k ) ) k is a bounded sequence and ( u k ) k a strictly increasing sequence of integers such that Sup α | k = 0 N - 1 θ ( k ) exp ( 2 i π α u k ) | = O ( N δ ) for some δ < 1 . Moreover we give explicit such sequences θ and u and we investigate in particular the case where θ is a q -multiplicative sequence.

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