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We provide a limiting absorption principle for the self-adjoint realizationsof Laplace operators corresponding to boundary conditions on (relatively openparts $\Sigma$ of) compact hypersurfaces $\Gamma=\partial\Omega$,$\Omega\subset{\mathbb{R}}^{n}$. For any of such self-adjoint operators we alsoprovide the generalized eigenfunctions and the scattering matrix; both theseobjects are written in terms of operator-valued Weyl functions. We make use ofa Krein-type formula which provides the resolvent difference between theoperator corresponding to self-adjoint boundary conditions on the hypersurfaceand the free Laplacian on the whole space ${\mathbb{R}}^{n}$. Our results applyto all standard examples of boundary conditions, like Dirichlet, Neumann,Robin, $\delta$ and $\delta'$-type, either assigned on $\Gamma$ or on$\Sigma\subset\Gamma$.

Limiting Absorption Principle, Generalized Eigenfunctions and Scattering Matrix for Laplace Operators with Boundary conditions on Hypersurfaces