An inverse problem for the matrix Schrodinger operator on the half-line with a general boundary condition

TL;DR

This paper addresses the inverse spectral problem for the matrix Schrödinger operator on the half-line with general self-adjoint boundary conditions, establishing uniqueness and providing a theoretical reconstruction method.

Contribution

It introduces a uniqueness theorem and a solvable main equation for reconstructing the operator from Weyl matrix data, extending inverse spectral theory.

Findings

Proved the uniqueness of the inverse spectral problem.

Derived the main equation for reconstruction.

Established the solvability of the inverse problem.

Abstract

In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the uniqueness theorem, and derive the main equation and prove its solvability, which yields a theoretical reconstruction algorithm of the inverse problem.