Inverse spectral problems for Dirac operators with summable matrix-valued potentials

TL;DR

This paper addresses the inverse spectral problem for Dirac operators with matrix-valued potentials in Lp spaces, providing a full spectral data characterization and a reconstruction method for the potentials.

Contribution

It offers a comprehensive description of spectral data and introduces a new method for reconstructing matrix-valued potentials from spectral information.

Findings

Complete spectral data characterization for Dirac operators with Lp potentials

A novel reconstruction method for the potentials from spectral data

Extension of inverse spectral theory to matrix-valued potentials in Lp spaces

Abstract

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.