Uniformity in the Wiener-Wintner theorem for nilsequences
Dynamical Systems
2013-02-12 v3
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.
Cite
@article{arxiv.1208.3977,
title = {Uniformity in the Wiener-Wintner theorem for nilsequences},
author = {Tanja Eisner and Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:1208.3977},
year = {2013}
}
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