Regular approximation of singular Sturm-Liouville problems with transmission conditions

In this paper we study regular approximation of singular Sturm-Liouville problems with transmission conditions. We construct all self-adjoint extensions of the minimal operators and the induced restriction operators. Using the abstract operator theory in the Hilbert space, we obtain that the spectrum of singular Sturm-Liouville problems with transmission conditions can be approximated by eigenvalues of a sequence of regular Sturm-Liouville problems with transmission conditions.