Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph

TL;DR

This paper investigates inverse spectral problems for Sturm-Liouville operators on star-shaped graphs and matrix operators, establishing conditions for solvability, local solvability, and stability.

Contribution

It provides necessary and sufficient conditions for the inverse spectral problems on star-shaped graphs and matrix operators, advancing understanding of their solvability and stability.

Findings

Derived conditions for inverse problem solvability

Proved local solvability and stability results

Extended analysis to matrix Sturm-Liouville operators

Abstract

The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the general self-adjoint form. We obtain necessary and sufficient conditions of solvability for these two inverse problems, and also prove their local solvability and stability.