Instability intervals of the Whittaker-Hill operator

2020/07/19 by Xu‐Dan Luo, Xu-Dan Luo, Luo, Xu-Dan
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP

paper · pdf · doi:10.48550/arxiv.2007.09575

arxiv created 2020/07/19 · openalex publication_date 2020/07/19 · arxiv updated 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On Exact Estimates of Instability Zones of the Hill's Equation with Locally Integrable Potential
• Some inverse problems associated with Hill operator
• Gap Labels and Asymptotic Gap Opening for Full Shifts
• A series of spectral gaps for the almost Mathieu operator with a small coupling constant
• Persistence of gaps in the spectrum of certain almost periodic operators