Inverse spectral problems for Dirac operators with summable potentials

TL;DR

This paper develops a comprehensive method for reconstructing Dirac operator potentials from spectral data when the potentials are integrable functions, advancing inverse spectral theory.

Contribution

It introduces a new algorithm for reconstructing potentials from spectral data for Dirac operators with summable potentials, solving the inverse spectral problem completely.

Findings

Reconstruction algorithm from two spectra or one spectrum with norming constants.

Complete solution to the inverse spectral problem for Dirac operators.

Potential recovery for potentials in $L_p(0,1)$.

Abstract

The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and the corresponding norming constants is established, and a complete solution of the inverse spectral problem is provided.