Recovery of the Schrödinger operator on the half-line from a particular set of eigenvalues (Q1750740)

Let \(\lambda_j(q,h_n),\; n\geq 1,\) be an eigenvalue of the Sturm-Liouville operator \[ -y''(x)+q(x)y(x)=\lambda y(x),\; x>0, \] \[ (1+x)q(x)\in L(0,\infty),\quad y'(0)-h_ny(0)=0, \] with fixed \(j\). It is proved that if the sequence \(\{h_n\}\) has a limit point, then the specification of \(\lambda_j(q,h_n)\), \(n\geq 1\), uniquely determines \(q\).