On the spectral properties of long-range perturbations of a class of block finite difference operators

We analyze spectral properties of a family of self-adjoint first-order finite difference operators acting on ${\mathrm{\ell }}^2(\mathbb{Z};{\mathbb{C}}^2)$ or ${\mathrm{\ell }}^2({\mathbb{Z}}_{+};{\mathbb{C}}^2)$. Applying the conjugate operator method, we prove the existence of limiting absorption principles and the absence of singular continuous spectrum for these operators. Our results cover classes of admissible long-range perturbations that have not been previously addressed.