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Weighted Birkhoff ergodic theorem with oscillating weights

Abstract : We consider sequences of Davenport type or Gelfond type and prove that sequences of Davenport exponent larger than 1/2 are good sequences of weights for the ergodic theorem, and that the ergodic sums weighted by a sequence of strong Gelfond property are well controlled almost everywhere. We prove that for any q-multiplicative sequence, the Gelfond property implies the strong Gelfond property and that sequences realized by dynamical systems can be fully oscillating and have the Gelfond property.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621998
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Soumis le : lundi 28 mars 2022 - 16:23:18
Dernière modification le : mercredi 14 septembre 2022 - 17:43:01

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Ai-Hua Fan. Weighted Birkhoff ergodic theorem with oscillating weights. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2019, 39 (5), pp.1275-1289. ⟨10.1017/etds.2017.81⟩. ⟨hal-03621998⟩

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