General Inverse Sturm-Liouville Problem with Symmetric Potential

The uniqueness theorems for an inverse nonselfadjoint Sturm-Liouville problem withsymmetric potential and general boundary conditions are proved. The spectral data using forunique reconstruction of Sturm-Liouville problems are a spectrum and six eigenvalues. The uniquenesstheorems for an inverse selfadjoint Sturm-Liouville problem with symmetric potential andnonseparated boundary conditions are proved also. These theorems use a spectrum and two (orthree) eigenvalues for unique reconstruction of Sturm-Liouville problems. The theorems generaliseG. Borg and N.Levinson classical results to the case Sturm-Liouville problem with general boundaryconditions. Schemes for unique reconstruction of the Sturm-Liouville Problems with symmetricpotential and general boundary conditions are given.