Singular Schrodinger operators as limits of point interaction Hamiltonians

In this paper we give results on the approximation of (generalized) Schrodinger operators of the form -Delta + mu for some finite Radon measure mu on R-d. For d = 1 we shall show that weak convergence of measures mu(n) to mu implies norm resolvent convergence of the operators -Delta + mu(n) to -Delta + mu. In particular Schrodinger operators of the form -Delta + mu for some finite Radon measure mu can be regularized or approximated by Hamiltonians describing point interactions. For d = 3 we shall show that a fairly large class of singular interactions can be regarded as limit of point interactions.