Solving Inverse Sturm-Liouville Problems with Transmission Conditions on Two Disjoint Intervals

In the present paper, some spectral properties of boundary value problems of Sturm-Liouville type on two disjoint bounded intervals with transmission boundary conditions are investigated. Uniqueness theorems for the solution of the inverse problem are proved, then we study the reconstructing of the coefficients of the Sturm-Liouville problem by the spectrtal mappings method.