Analyticity properties of the scattering matrix for matrix Schr\"odinger operators on the discrete line

Abstract

Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the band edge singularities and allows to prove a Levinson-type theorem. The main algebraic tool are the plane wave transfer matrices.