Inverse problems for Jacobi operators IV: Interior mass-spring perturbations of semi-infinite systems

TL;DR

This paper investigates how to recover semi-infinite mass-spring systems from the spectra of original and perturbed systems, providing conditions for spectral characterization and system reconstruction.

Contribution

It introduces necessary and sufficient conditions for identifying and reconstructing semi-infinite mass-spring systems from spectral data after interior perturbations.

Findings

Recovery of the original system from two spectra.

Necessary and sufficient spectral conditions established.

Method for system reconstruction from spectral data.

Abstract

This work gives results on the interplay of the spectra of two Jacobi operators corresponding to an infinite mass-spring system and a modification of it obtained by changing one mass and one spring of the system. It is shown that the system can be recovered from these two spectra. Necessary and sufficient conditions for two sequences to be the spectra of the mass-spring system and the perturbed one are provided.