Inverse spectral problem for singular AKNS operator on [0,1]

Abstract

We consider an inverse spectral problem for a class of singular AKNS operators $H\_a,a\in \mathbb{N}$ with an explicit singularity. We construct for each $a\in \mathbb{N}$, a standard map ${\lambda }^a\times {\kappa }^a$ with spectral data ${\lambda }^a$ and some norming constant ${\kappa }^a$. For $a=0$, ${\lambda }^a\times {\kappa }^a$ was known to be a local coordinate system on $\lr\times\lr$. Using adapted transformation operators, we extend this result to any non-negative integer $a$, give a description of isospectral sets and we obtain a Borg-Levinson type theorem.

31 pages