On inverse spectral problems for self-adjoint Dirac operators with general boundary conditions

TL;DR

This paper investigates inverse spectral problems for self-adjoint Dirac operators with general boundary conditions, aiming to reconstruct potentials and boundary data from spectral information.

Contribution

It introduces a method to recover potentials and boundary conditions of Dirac operators using eigenvalues and norming matrices, expanding inverse spectral theory.

Findings

Reconstruction of potentials from spectral data

Recovery of boundary conditions from eigenvalues

Extension to general boundary conditions

Abstract

We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary conditions of the operator from its eigenvalues and suitably defined norming matrices.