Spectral estimates for periodic fourth order operators
| dc.creator | Badanin, Andrey | |
| dc.creator | Korotyaev, Evgeny | |
| dc.date | 2008-08-05 | |
| dc.date.accessioned | 2026-07-07T09:54:43Z | |
| dc.date.available | 2026-07-07T09:54:43Z | |
| dc.description | We consider the operator $H={d^4dt^4}+{ddt}p{ddt}+q$ with 1-periodic coefficients on the real line. The spectrum of $H$ is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms of the Lyapunov function, which is analytic on a two-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov function for the scalar case. We describe the spectrum of $H$ in terms of periodic, antiperiodic eigenvalues, and so-called resonances. We prove that 1) the spectrum of $H$ at high energy has multiplicity two, 2) the asymptotics of the periodic, antiperiodic eigenvalues and of the resonances are determined at high energy, 3) for some specific $p$ the spectrum of $H$ has an infinite number of gaps, 4) the spectrum of $H$ has small spectral band (near the beginner of the spectrum) with multiplicity 4 and its asymptotics are determined as $p\to 0, q=0$. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/0808.0588 | |
| dc.identifier | http://arxiv.org/abs/0808.0588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166423 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34L20; 34L40 | |
| dc.title | Spectral estimates for periodic fourth order operators | |
| dc.type | text |