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Uniformity in the polynomial Wiener–Wintner theorem

Published online by Cambridge University Press:  10 July 2006

NIKOS FRANTZIKINAKIS
NIKOS FRANTZIKINAKIS
Affiliation:
Einstein Drive, Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail: [email protected])
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Abstract

In 1993, E. Lesigne 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 4 , August 2006 , pp. 1061 - 1071
Copyright
2006 Cambridge University Press

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