Partial Inverse Spectral Problems for Sturm-Liouville Operators with Frozen Arguments on a Star-Shaped Graph

TL;DR

This paper addresses a partial inverse spectral problem for Sturm-Liouville operators on a star-shaped graph, reconstructing unknown potentials on one edge from spectral data, with a constructive algorithm based on Riesz basis properties.

Contribution

It introduces a novel method for reconstructing unknown potentials on a graph edge using spectral data and a Riesz basis approach, advancing inverse spectral theory on graphs.

Findings

Reconstruction algorithm for unknown potential on a graph edge

Use of Riesz basis property for spectral data analysis

Successful application to star-shaped graph models

Abstract

This paper is devoted to the study of a partial inverse spectral problem for Sturm-Liouville operators with frozen arguments on a star-shaped graph. The potentials are assumed to be known a priori on all edges except one, and the objective is to reconstruct the unknown potential on the remaining edge using a subset of the spectral data. A constructive algorithm for solving this problem is presented, which relies on the Riesz basis property of a system of vector functions.