Inverse Spectral Analysis of Singular Radial AKNS Operators

Abstract

We study an inverse spectral problem for singular AKNS operators based on spectral data associated with two distinct values of the effective angular momentum parameter $\kappa$. Our main focus is the local inverse problem near the zero potential. For the pairs $({\kappa }_1,{\kappa }_2)=(0,1)$, $(1,2)$ and $(0,3)$, we establish local uniqueness. For $(0,2)$, we prove that the Fréchet differential of the spectral map at the origin is injective, while the question whether its range is closed remains open.

50 pages