Essential Spectra of Singular Matrix Difference Systems of Mixed Order

ABSTRACT This paper is concerned with a class of singular matrix difference systems of mixed order. By transforming them into the corresponding singular Hamiltonian systems, the limit point and limit circle classification of them is obtained, relationships among the associated maximal, pre‐minimal, and minimal subspaces are derived, the singular part of the essential spectrum of such a system is characterized in terms of properties of that of the corresponding Hamiltonian system. In addition, several sufficient conditions are obtained for points to be in the regular part of the essential spectrum.