|Publisher DOI:||10.1007/s11040-016-9230-0||Title:||On eigenvalue bounds for a general class of Sturm-Liouville operators||Language:||English||Authors:||Seifert, Christian||Keywords:||Eigenvalue problem; Jacobi operators; Quasiperiodic operators; Sturm-Liouville operators; Transfer matrices||Issue Date:||21-Nov-2016||Publisher:||Springer Science + Business Media B.V.||Source:||Mathematical Physics Analysis and Geometry 19 (4): 25 (2016)||Abstract (english):||
We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative Gordon condition, we prove a bound on eigenvalues for the corresponding operator in Lp, for 1 ≤ p< ∞. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.
|URI:||http://hdl.handle.net/11420/11146||ISSN:||1572-9656||Journal:||Mathematical physics, analysis and geometry||Institute:||Mathematik E-10||Document Type:||Article|
|Appears in Collections:||Publications without fulltext|
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