Continuity of the measure of the spectrum for discrete quasiperiodic operators
| dc.creator | Jitomirskaya, S. Ya. | |
| dc.creator | Krasovsky, I. V. | |
| dc.date | 2001-07-08 | |
| dc.date | 2002-05-30 | |
| dc.date.accessioned | 2026-07-07T04:42:32Z | |
| dc.date.available | 2026-07-07T04:42:32Z | |
| dc.description | We study discrete Schroedinger operators $(H_{α,θ}ψ)(n)= ψ(n-1)+ψ(n+1)+f(αn+θ)ψ(n)$ on $l^2(Z)$, where $f(x)$ is a real analytic periodic function of period 1. We prove a general theorem relating the measure of the spectrum of $H_{α,θ}$ to the measures of the spectra of its canonical rational approximants under the condition that the Lyapunov exponents of $H_{α,θ}$ are positive. For the almost Mathieu operator ($f(x)=2λ\cos 2πx$) it follows that the measure of the spectrum is equal to $4|1-|λ||$ for all real $θ$, $λ\ne\pm 1$, and all irrational $α$. | |
| dc.description | 10 pages, small changes, to appear in Math.Res.Lett | |
| dc.identifier | https://arxiv.org/abs/math/0107061 | |
| dc.identifier | http://arxiv.org/abs/math/0107061 | |
| dc.identifier | Math.Res.Lett. 9 (2002) 413-422 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61820 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | Continuity of the measure of the spectrum for discrete quasiperiodic operators | |
| dc.type | text |