Instability intervals of the Whittaker-Hill operator

Xu-Dan Luo

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arXiv · 2007.09575

Instability intervals of the Whittaker-Hill operator

Xu-Dan Luo

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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.

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Xu-Dan Luo. 2020-07-19. Instability intervals of the Whittaker-Hill operator. https://arxiv.org/abs/2007.09575

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