On the solvability of inverse Sturm–Liouville problems with self-adjoint boundary conditions

Abstract

Theorems on the existence and uniqueness of a solution of the inverse Sturm–Liouville problem with self-adjoint nonseparated boundary conditions are proved. As spectral data two spectra and two eigenvalues are used. The theorems generalize the Levitan–Gasymov solvability theorem and Borg’s uniqueness theorem to the case of general boundary conditions.