Discrete Laplacian in a half-space with a periodic surface potential : an overview on analytical investigations (Spectral and Scattering Theory and Related Topics)

In this conference proceeding's paper we summarize some recent investigations on a scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. This material is borrowed from a joint paper [9] with H.S. Nguyen and R. Tiedra de Aldecoa. For more precise statements and details, we refer to this reference