Inverse eigenvalue problems for rank one perturbations of the Sturm-Liouville operator

This article is concerned with the inverse eigenvalue problem for rank one perturbations of the Sturm-Liouville operator. I obtain the relationship between the spectra of the Sturm-Liouville operator and its rank one perturbations, and from the spectra I reconstruct the perturbed operators, provided that the potential is known a priori.