Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces

We provide a limiting absorption principle for the self-adjoint realizations of Laplace operators corresponding to boundary conditions on (relatively open parts Sigma of) compact hypersurfaces Gamma = partial derivative Omega,Omega subset of R-n. For any of such self-adjoint operators we also provide the generalized eigenfunctions and the scattering matrix; both these objects are written in terms of operator-valued Weyl functions. We make use of a Krein-type formula which provides the resolvent difference between the operator corresponding to self-adjoint boundary conditions on the hypersurface and the free Laplacian on the whole space R-n. Our results apply to all standard examples of boundary conditions, like Dirichlet, Neumann, Robin, delta and delta'-type, either assigned on Gamma or on Sigma subset of Gamma.