Regular approximation of singular second-order differential expressions

In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression l(y) = 1/omega [-(py')' + qy]. If 0 is in the resolvent of the original operator, then the construction guarantees that 0 is a point of the resolvent set of the approximating operators. The notion of strong resolvent convergence is generalized and we prove the strong resolvent convergence of the approximations. (C) 2003 Elsevier Inc. All rights reserved.