Generating spectral gaps by geometry
| dc.creator | Lledó, Fernando | |
| dc.creator | Post, Olaf | |
| dc.date | 2004-06-15 | |
| dc.date | 2005-06-23 | |
| dc.date.accessioned | 2026-07-07T04:31:15Z | |
| dc.date.available | 2026-07-07T04:31:15Z | |
| dc.description | Motivated by the analysis of Schrödinger operators with periodic potentials we consider the following abstract situation: Let $Δ_X$ be the Laplacian on a non-compact Riemannian covering manifold $X$ with a discrete isometric group $Γ$ acting on it such that the quotient $X/Γ$ is a compact manifold. We prove the existence of a finite number of spectral gaps for the operator $Δ_X$ associated with a suitable class of manifolds $X$ with non-abelian covering transformation groups $Γ$. This result is based on the non-abelian Floquet theory as well as the Min-Max-principle. Groups of type I specify a class of examples satisfying the assumptions of the main theorem. | |
| dc.description | Some mistakes corrected (still 12 pages, 1 figure) | |
| dc.identifier | https://arxiv.org/abs/math-ph/0406032 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0406032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57748 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 58J50 | |
| dc.title | Generating spectral gaps by geometry | |
| dc.type | text |