Inverse Spectral Problems for Sturm-Liouville Operators on Hedgehog-type Graphs with General Matching Conditions

TL;DR

This paper addresses inverse spectral problems for Sturm-Liouville operators on hedgehog-type graphs, establishing uniqueness and solution construction methods for recovering differential coefficients from spectral data.

Contribution

It introduces a new approach for solving inverse spectral problems on complex graph structures with general matching conditions, including a proof of uniqueness.

Findings

Proved a uniqueness theorem for the inverse problem.

Developed a procedure for reconstructing coefficients from spectral data.

Extended inverse spectral theory to hedgehog-type graphs with general matching conditions.

Abstract

Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation from the spectral data. For this inverse problem we prove a uniqueness theorem and provide a procedure for constructing its solution.