Abstract
We give a criterion of asymptotic completeness and provide a representation of the scattering matrix for the scattering couple (A0,A), where A0 and A are semi-bounded self-adjoint operators in L2(M,B,m) such that the set {u∈dom(A0)∩dom(A):A0u=Au} is dense. No sort of trace-class condition on resolvent differences is required. Applications to the case in which A0 corresponds to the free Laplacian in L2(Rn) and A describes the Laplacian with self-adjoint boundary conditions on rough compact hypersurfaces are given.
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