Analyticity and uniform stability in the inverse spectral problem for Dirac operators

TL;DR

This paper demonstrates that the process of reconstructing square integrable potentials for Dirac operators from spectral data is both analytic and uniformly stable, ensuring reliable inverse spectral analysis.

Contribution

It establishes the analyticity and uniform stability of the inverse spectral mapping for Dirac operators, a significant advancement in inverse spectral theory.

Findings

Inverse spectral mapping is analytic.

Reconstruction is uniformly stable.

Applicable to potentials in L^2([0,1]) for Dirac operators.

Abstract

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.