On the missing eigenvalue problem for an inverse Sturm-Liouville problem (Q1019132)

Let \(\lambda_n, n\geq 0,\) be the eigenvalues of the boundary value problem \[ -u''+q(x)u=\lambda u,\; u'(0)-hu(0)=u'(\pi)+Hu(\pi)=0. \] Let \(q(x), x\in[0,\pi/2], h\) and \(H\) are known a priori. Fix \(m\geq 0.\) It is proved that the specification of \(\lambda_n,\; n\geq 0,\; n\neq m,\) uniquely determines \(q(x), x\in[\pi/2,\pi].\)