Regular approximation of singular Sturm–Liouville problems with transmission conditions

摘要

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.