Asymptotic completeness and S-matrix for singular perturbations

We give a criterion of asymptotic completeness and provide a representation of the scattering matrix for the scattering couple (A(0), A), where A(0) and A are semi-bounded self-adjoint operators in L-2(M, B, m) such that the set {u is an element of dom(A(0)) boolean AND dom(A) : A(0)u = Au} is dense. No sort of trace-class condition on resolvent differences is required. Applications to the case in which A(0) corresponds to the free Laplacian in L-2(R-n) and A describes the Laplacian with self-adjoint boundary conditions on rough compact hypersurfaces are given. (C) 2019 Elsevier Masson SAS. All rights reserved.