On inverse spectral problem for non-selfadjoint Sturm-Liouville operator on a finite interval (Q2642146)

The inverse spectral problem is studied for the Sturm-Liouville operator \[ \ell y:= -y''+q(x)y, \qquad 0<x<\pi, \] with the boundary conditions \[ y'(0)-hy(0)=y'(\pi)+Hy(\pi)=0, \] where \(q(x)\) is a complex-valued integrable function and \(h,H\) are complex numbers. Generalized weight numbers are introduced. A uniqueness theorem is proved and a constructive procedure for solving the inverse problem based on the method of spectral mappings is given.