Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space. This work includes a detailed spectral analysis of the perturbed Laplacian and the construction and study of the corresponding objects pertaining to scattering theory, including the entries of the scattering matrix.
Sher et al. (Sun,) studied this question.