A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages
Dynamical Systems
2015-08-06 v2
Abstract
We show that a -linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform -linear nilsequence Wiener-Wintner theorem on that system. The assumption is known to hold for arbitrary systems and (due to Bourgain) and for distal systems and arbitrary (due to Huang, Shao, and Ye).
Cite
@article{arxiv.1504.04647,
title = {A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages},
author = {Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:1504.04647},
year = {2015}
}
Comments
v2: 4 pages, characterization of good weights for L^2 convergence added, uniformity seminorm in the main result corrected