2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69520We develop the basic theory of matrix-valued Weyl-Titchmarsh M-functions and the associated Green's matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.30 pages, to appear in J. Comput. Appl. MathSpectral Theory34B20; 39A10; 34B27; 39A70text