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Uniformity in the polynomial Wiener-Wintner theorem. (English) Zbl 1101.37008
Summary: In 1993, {\it E. Lesigne} [ibid. 13, 767--784 (1993; Zbl 0803.47013)] proved a polynomial extension of the Wiener-Wintner theorem and asked two questions: does this result have a uniform counterpart and can an assumption of total ergodicity be replaced by ergodicity? The purpose of this article is to answer these questions, the first one positively and the second one negatively.

37A30Ergodic theorems, spectral theory, Markov operators
28D05Measure-preserving transformations
37A20Orbit equivalence, cocycles, ergodic equivalence relations
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