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Spectral analysis for linear semi‐infinite mass‐spring systems
Author(s) -
Rio Rafael del,
Silva Luis O.
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400044
Subject(s) - mathematics , eigenvalues and eigenvectors , perturbation (astronomy) , operator (biology) , spectral analysis , mathematical analysis , jacobi operator , rank (graph theory) , spectrum (functional analysis) , spring (device) , jacobi polynomials , physics , combinatorics , quantum mechanics , orthogonal polynomials , biochemistry , spectroscopy , transcription factor , gene , thermodynamics , chemistry , repressor
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.