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arXiv · 1504.04647

A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages

Pavel Zorin-Kranich
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Abstract

We show that a $k$-linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform $k$-linear nilsequence Wiener-Wintner theorem on that system. The assumption is known to hold for arbitrary systems and $k=2$ (due to Bourgain) and for distal systems and arbitrary $k$ (due to Huang, Shao, and Ye).

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Pavel Zorin-Kranich. 2015-04-17. A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages. https://arxiv.org/abs/1504.04647

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