On the spectrum of the Schrodinger operator with periodic surface potential

We consider a discrete Schrodinger operator H = -Delta + V acting in l(2)(Z (d)), with periodic potential V supported by the subspace 'surface' {0} x Z (d2). We prove that the spectrum of H is purely absolutely continuous, and that surface waves oscillate in the longitudinal directions to the 'surface '. We also find an explicit formula for the generalized spectral shift func tion introduced by the author in Helv. Phys. Acta. 72 (1999), 93-122.