On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems

We study discrete, generally non-self-adjoint Hamiltonian systems, defining Weyl-Sims sets, which replace the classical Weyl circles, and a matrix-valued M-function on suitable cone-shaped domains in the complex plane. Furthermore, we characterise realisations of the corresponding differential operator and its adjoint, and construct their resolvents.