Inverse Sturm-Liouville problems and Hill's equation (Q1072693)

One considers a Sturm-Liouville operator on \(L^ 2(0,\infty):\) \[ Lu=- u''+q(x)u,\quad u(0)\cos \alpha +u'(0)\sin \alpha =0. \] The paper is related to the following general problem: does the spectrum of this operator determine the potential q(x) and the angle \(\alpha\) ? The authors consider \(\pi\)-periodic potentials. Let \(\Delta\) (\(\lambda)\) be the discriminant of the associated Hill's equation: \(u''+(\lambda - q(x))u=0\). One of the results of the paper says that, under certain conditions, the discriminant \(\Delta\) (\(\lambda)\) and the point spectrum of L determine the potential q(x) and the angle \(\alpha\).