A note on eigenvalues of a class of singular continuous and discrete linear Hamiltonian systems

2018/08/01 by Hao Zhu, Zhu, Hao · 1 citation
Mathematics · Computer Science · #Spectral Theory in Mathematical Physics #Matrix Theory and Algorithms #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1808.00397

Abstract

In this paper, we show that the analytic and geometric multiplicities of an eigenvalue of a class of singular linear Hamiltonian systems are equal, where both endpoints are in the limit circle cases. The proof is fundamental and is given for both continuous and discrete Hamiltonian systems. The method used in this paper also works for both endpoints are regular, or one endpoint is regular and the other is in the limit circle case.

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• Discrete Sturm-Liouville problems: singularity of the n-th eigenvalue with application to Atkinson type

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