Quantitative version of Beurling-Helson theorem
Classical Analysis and ODEs
2014-01-20 v1 Combinatorics
Number Theory
Abstract
It is proved that any continuous function f on the unit circle such that the sequence e^{in f}, n=1,2,... has small Wiener norm \| e^{in f} \|_A = o (\frac{\log^{1/22} |n|}{(\log \log |n|)^{3/11}}), is linear. Moreover, we get lower bounds for Wiener norm of characteristic functions of subsets from Z_p in the case of prime p.
Cite
@article{arxiv.1401.4429,
title = {Quantitative version of Beurling-Helson theorem},
author = {Sergei V. Konyagin and Ilya D. Shkredov},
journal= {arXiv preprint arXiv:1401.4429},
year = {2014}
}
Comments
15 pages