On a solution to the inverse problem of determination of a singular Sturm-Liouville equation from two spectra (Q1594342)

Consider the Sturm-Liouville equation \[ -y''+q(x)y=\mu y, \quad 0<x<\pi, \tag{1} \] where the potential \(q\) is real and satisfies the condition \(\int_0^\pi x|q(x)|dx<\infty.\) The author provides a solution to the inverse problem of recovering \(q\) from two spectra of the boundary value problems for equation (1) with the boundary conditions \(y(0)=y(\pi)=0\) and \(y(0)=y'(\pi)-hy(\pi)=0\). The inverse scattering problem is also considered.