On the spectral and scattering theory of the Schrodinger operator with surface potential

We consider a discrete Schrodinger operator H = -Delta + V acting in l(2)(Z (d+1)), with potential V supported by the subspace Z(d) X {0}. We prove tha t sigma(-Delta) = [-2(d + 1), 2(d + 1)] is contained in the absolutely cont inuous spectrum of H. For this we develop a scattering theory for H. We emp hasize the fact that this result applies to arbitrary potentials, so it dep ends on the structure of the problem rather than on a particular choice of the potential.