An inverse eigenvalue problem for a nonlocal Sturm-Liouville operator

Abstract

This paper is concerned with the inverse eigenvalue problem for a nonlocal Sturm-Liouville operator generated by its rank one perturbations. We give a necessary and sufficient condition that a sequence of real numbers is the spectrum of a nonlocal Sturm-Liouville operator, provided that the potential is known a priori. An explicit algorithm for constructing all such operators is also provided.