Uniform stability for the matrix inverse Sturm-Liouville problems

TL;DR

This paper proves the uniform stability of the inverse spectral problem for matrix Sturm-Liouville operators on finite intervals and star-shaped graphs, providing bounds on spectral data differences and potential reconstructions.

Contribution

It introduces a constructive method based on spectral mappings to establish uniform stability for inverse matrix Sturm-Liouville problems on finite intervals and graphs.

Findings

Established uniform stability bounds for inverse spectral data

Developed a constructive spectral mapping approach

Extended results to star-shaped graph configurations

Abstract

In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded and, consequently, the uniform estimates hold for the differences of the matrix potentials and of the corresponding coefficients of the boundary conditions. Our approach is based on a constructive procedure for solving the inverse problem by developing ideas of the method of spectral mappings. In addition, we apply our technique to obtain the uniform stability of the inverse Sturm-Liouville problem on the star-shaped graph.