Instability intervals of the Whittaker-Hill operator
Spectral Theory
2020-07-21 v1
Abstract
The Hill operator admits a band gap structure. As a special case, like the Mathieu operator, one has only open gaps, however, the instability intervals of the Whittaker-Hill operator may be open or closed. In 2007, P. Djakov and B. Mityagin gave the asymptotics of band gaps for a special Whittaker-Hill operator [P. Djakov and B. Mityagin, J. Funct. Anal., 242, 157-194 (2007).]. In this paper, a more general Whittaker-Hill operator is considered and the asymptotics of the instability intervals are studied.
Cite
@article{arxiv.2007.09575,
title = {Instability intervals of the Whittaker-Hill operator},
author = {Xu-Dan Luo},
journal= {arXiv preprint arXiv:2007.09575},
year = {2020}
}