Regular approximations of singular Sturm-Liouville problems

Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of eigenvalues from the individual members of {Sr} has to converge to an eigenvalue of S (iii) in the general case when S is bounded below, property (ii) holds for all eigenvalues below the essential spectrum of S.