Weighted Birkhoff ergodic theorem with oscillating weights

Aihua Fan

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arXiv · 1705.02501

Weighted Birkhoff ergodic theorem with oscillating weights

Aihua Fan

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Abstract

We consider sequences of Davenport type or Gelfond type and prove that sequences of Davenport exponent larger than $\frac{1}{2}$ are good sequences of weights for the ergodic theorem, and that the ergodic sums weighted by a sequence of strong Gelfond property is 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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Aihua Fan. 2017-05-06. Weighted Birkhoff ergodic theorem with oscillating weights. https://arxiv.org/abs/1705.02501

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