Diophantine estimates on shifts of trigonometric polynomials on $\mathbb{T}^d$
Mathematical Physics
2024-05-30 v2 Dynamical Systems
math.MP
Number Theory
Abstract
We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus , as well as that of their square roots. These estimates arise from the spectral analysis of the quasi-periodic Schr\"odinger and the quasi-periodic wave operators. They have applications to the nonlinear quasi-periodic Schr\"odinger equations (NLS) and the nonlinear quasi-periodic wave equations (NLW). One could now, for example, extend the result of Bourgain (Geom. Funct. Anal. 17(3): 682-706, 2007) to the nonlinear setting.
Keywords
Cite
@article{arxiv.2309.12666,
title = {Diophantine estimates on shifts of trigonometric polynomials on $\mathbb{T}^d$},
author = {Yunfeng Shi and W. -M. Wang},
journal= {arXiv preprint arXiv:2309.12666},
year = {2024}
}
Comments
It is combined in arXiv:2405.17513 and is not intended to be published