Inverse spectral problem for radial Schr\"{o}dinger 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.