Uniformity in the Wiener-Wintner theorem for nilsequences

Published 20 Aug 2012 in math.DS | (1208.3977v3)

Abstract: We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.

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