Gap Labelling for Almost Periodic Sturm-Liouville Operators
Spectral Theory
2026-02-10 v2 Dynamical Systems
Abstract
In this paper, we introduce a rotation number for almost periodic Sturm-Liouville operators in the spirit of Johnson and Moser. We then prove the gap labelling theorem in terms of rotation numbers for the operator in question. To do this, we rigorously prove the almost periodicity of Green's functions.
Cite
@article{arxiv.2601.18312,
title = {Gap Labelling for Almost Periodic Sturm-Liouville Operators},
author = {Gerald Teschl and Yifei Wang and Bing Xie and Zhe Zhou},
journal= {arXiv preprint arXiv:2601.18312},
year = {2026}
}