On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potentials
| dc.creator | Batchenko, Volodymyr | |
| dc.creator | Gesztesy, Fritz | |
| dc.date | 2003-12-10 | |
| dc.date.accessioned | 2026-07-07T05:03:44Z | |
| dc.date.available | 2026-07-07T05:03:44Z | |
| dc.description | We characterize the spectrum of one-dimensional Schrödinger operators H=-d^2/dx^2+V with quasi-periodic complex-valued algebro-geometric potentials V (i.e., potentials V which satisfy one (and hence infinitely many) equation(s) of the stationary Korteweg-de Vries (KdV) hierarchy) associated with nonsingular hyperelliptic curves. The corresponding problem appears to have been open since the mid-seventies. The spectrum of H coincides with the conditional stability set of H and can explicitly be described in terms of the mean value of the inverse of the diagonal Green's function of H. As a result, the spectrum of H consists of finitely many simple analytic arcs and one semi-infinite simple analytic arc in the complex plane. Crossings as well as confluences of spectral arcs are possible and discussed as well. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312200 | |
| dc.identifier | http://arxiv.org/abs/math/0312200 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69539 | |
| dc.subject | Spectral Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 34L05; 35Q53; 58F07; 34L40; 35Q51 | |
| dc.title | On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potentials | |
| dc.type | text |