Spectral analysis for linear semi‐infinite mass‐spring systems |
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Authors: | Luis O Silva |
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Institution: | 1. Departamento de Física, Matemática Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México C. 2. P, México D. 3. F. |
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Abstract: | We study how the spectrum of a Jacobi operator changes when this operator is modified by a certain finite rank perturbation. The operator corresponds to an infinite mass‐spring system and the perturbation is obtained by modifying one interior mass and one spring of this system. In particular, there are detailed results of what happens in the spectral gaps and which eigenvalues do not move under the modifications considered. These results were obtained by a new tecnique of comparative spectral analysis and they generalize and include previous results for finite and infinite Jacobi matrices. |
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Keywords: | Jacobi matrices spectrum infinite mass‐spring system 47A75 47B36 |
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