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1998•Proceedings of the Royal Society of Edinburgh Section A MathematicsRequires access

Eigenvalue ratios and eigenvalue gaps of Sturm–Liouville operators

Chun‐Kong Law, Yu-Ling Huang

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Abstract

We prove optimal lower bounds for arbitrary eigenvalue ratios (μm/μn) of the Sturm–Liouville operator with Dirichlet and Neumann boundary conditions. These imply optimal bounds for the eigenvalue gaps (μm – μn) of the corresponding problem. The method can be generalised to consider general separated endpoint boundary conditions.

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What this paper is about

We prove optimal lower bounds for arbitrary eigenvalue ratios (μm/μn) of the Sturm–Liouville operator with Dirichlet and Neumann boundary conditions. These imply optimal bounds for the eigenvalue gaps (μm – μn) of the corresponding problem. The method can be generalised to consider general separated endpoint boundary conditions.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove optimal lower bounds for arbitrary eigenvalue ratios (μm/μn) of the Sturm–Liouville operator with Dirichlet and Neumann boundary conditions. These imply optimal bounds for the eigenvalue gaps (μm – μn) of the corresponding problem. The method can be generalised to consider general separated endpoint boundary conditions.

Key concepts: Sturm–Liouville theory, Eigenvalues and eigenvectors, Mathematics, Dirichlet boundary condition, Operator (biology), Boundary (topology), Dirichlet distribution, Boundary value problem

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