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 (y) = 1 w −(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.  2003 Elsevier Inc. All rights reserved.