J -Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems

Abstract

This paper is concerned with formally $J$-self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All the $J$-self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all the $J$-self-adjoint subspace extensions are given in the limit point and limit circle cases.