Inverse spectral problem for radial Schrödinger operator on [0, 1]

Abstract

For a class of singular Sturm-Liouville equations on the unit interval with explicit singularity $a(a+1)/x^2,a\in \mathbb{N}$, we consider an inverse spectral problem. Our goal is the global parametrization of potentials by spectral data noted by ${\lambda }^a$, and some norming constants noted by ${\kappa }^a$. For $a=0$ and $a=1$, ${\lambda }^a\times {\kappa }^a$ was already known to be a global coordinate system on $\lr$. With the help of transformation operators, we extend this result to any non-negative integer $a$ and give a description of isospectral sets.

22 pages