An inverse problem for a differential operator with a mixed spectrum (Q762328)

The operator \(Ly=-y''+q(t)y\) on the interval [0,\(\infty)\) with a boundary condition sin \(\alpha\) y(0)\(+\cos \alpha y'(0)=0\), under the assumption \(q(t+\pi)=q(t)\) is investigated. It is shown that the specification of only a finite number of eigenvalues leads to a unique determination of q(t), provided the continuous spectrum of L has only a finite number of finite intervals and one infinite interval.