# American Institute of Mathematical Sciences

August  2013, 33(8): 3497-3516. doi: 10.3934/dcds.2013.33.3497

## Uniformity in the Wiener-Wintner theorem for nilsequences

 1 KdV Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam 2 Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, Netherlands

Received  May 2012 Revised  October 2012 Published  January 2013

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.
Citation: Tanja Eisner, Pavel Zorin-Kranich. Uniformity in the Wiener-Wintner theorem for nilsequences. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3497-3516. doi: 10.3934/dcds.2013.33.3497
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