Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions

Xijun Hu; Penghui Wang

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arXiv · 1504.01817

Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions

Xijun Hu·Penghui Wang

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Abstract

Let $\lambda_j$ be the $j$-th eigenvalue of Sturm-Liouville systems with separated boundary conditions, we build up the Hill-type formula, which represent $\prod\limits_{j}(1-\lambda_j^{-1})$ as a determinant of finite matrix. This is the first attack on such a formula under non-periodic type boundary conditions. Consequently, we get the Krein-type trace formula based on the Hill-type formula, which express $\sum\limits_{j}{1\over \lambda_j^m}$ as trace of finite matrices. The trace formula can be used to estimate the conjugate point alone a geodesic in Riemannian manifold and to get some infinite sum identities.

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BibTeX RIS

Xijun Hu, Penghui Wang. 2015-04-08. Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions. https://arxiv.org/abs/1504.01817

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