2015/05/28 by Hao Zhu, Zhu, Hao, Yuming Shi +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Matrix Theory and Algorithms #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP
paper · pdf · doi:10.48550/arxiv.1505.07536
32 pages, 3 figures
arxiv created 2015/05/28 · openalex publication_date 2015/05/28 · arxiv updated 2015/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper is concerned with continuous dependence of the n-th eigenvalue on self-adjoint discrete Sturm-Liouville problems. The n-th eigenvalue is considered as a function in the space of the problems. A necessary and sufficient condition for all the eigenvalue functions to be continuous and several properties of the eigenvalue functions in a set of the space of the problems are given. They play an important role in the study of continuous dependence of the n-th eigenvalue function on the problems. Continuous dependence of the n-th eigenvalue function on the equations and on the boundary conditions is studied separately. Consequently, the continuity and discontinuity of the n-th eigenvalue function are completely characterized in the whole space of the problems. Especially, asymptotic behaviors of the n-th eigenvalue function near each discontinuity point are given.