Tanja Eisner, Pavel Zorin-Kranich
Published 2012-08-20, updated 2012-10-22Version 3
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.
Comments: v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v2
Journal: Discrete Contin. Dyn. Syst. 33 (2013) 3497-3516
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