Inverse problems for Jacobi operators III: Mass-spring perturbations of semi-infinite systems

TL;DR

This paper investigates the spectral properties of semi-infinite mass-spring systems and their perturbations, providing conditions for reconstructing the system from spectral data and analyzing the effects of changing the first mass and spring.

Contribution

It offers new theoretical results on the relationship between spectra of original and perturbed systems and establishes criteria for spectral reconstruction.

Findings

Derived necessary and sufficient conditions for spectral sequences

Analyzed the spectral interplay between original and perturbed systems

Provided methods for reconstructing the system from spectral data

Abstract

Consider an infinite linear mass-spring system and a modification of it obtained by changing the first mass and spring of the system. We give results on the interplay of the spectra of such systems and on the reconstruction of the system from its spectrum and the one of the modified system. Furthermore, we provide necessary and sufficient conditions for two sequences to be the spectra of the mass-spring system and the perturbed one.