On the solvability of inverse Sturm-Liouville problems with self-adjoint boundary conditions (Q294346)

The boundary value problem \[ \begin{aligned} -y''+q(x)y&=\lambda y,\; q\in L(0,\pi), \\ y'(0)+a_{11}y(0)+a_{13}y(\pi)&=y'(\pi)+a_{23}y(\pi)-a_{13}y(0)=0 \end{aligned} \] is considered, where \(a_{ij}\) are complex numbers. The authors study the inverse problem of recovering the numbers \(a_{ij}\) from the given eigenvalues, provided that the function \(q(x)\) is known a priori. They obtain uniqueness results and discuss the solvability of the problem. In the paper there are no results on inverse Sturm-Liouville problems, because the potential \(q\) is known.