The inverse spectral problem for radial Schrödinger operators on [formula omitted

Abstract

We consider an inverse spectral problem for a class of singular Sturm–Liouville operators on the unit interval with explicit singularity a ( a + 1 ) / x 2 , a ∈ N , related to the Schrödinger operator with a radially symmetric potential. The purpose of this paper is the global parametrization of potentials by the spectral data λ a and some norming constants κ a . For a = 0 or 1, λ a × κ a is already known to be a global coordinate system on L R 2 ( 0 , 1 ) . Using some transformation operators, we show that this result holds for any non-negative integer a; moreover, we give a description of the isospectral sets.