On eigenvalue bounds for a general class of Sturm-Liouville operators

Christian Seifert

doi:10.1007/s11040-016-9230-0

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arXiv · 1608.02219

On eigenvalue bounds for a general class of Sturm-Liouville operators

Christian Seifert

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Abstract

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 $L_p$, for $1\leq p<\infty$. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.

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BibTeX RIS

Christian Seifert. 2016-08-07. On eigenvalue bounds for a general class of Sturm-Liouville operators. https://doi.org/10.1007/s11040-016-9230-0

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