Abstract
The paper is concerned with the essential spectral points of singular discrete linear Hamiltonian systems. Several sufficient conditions for a real point to be in the essential spectrum are obtained in terms of the number of linearly independent square‐summable solutions of the corresponding homogeneous linear system, and a sufficient and necessary condition for a real point to be in the essential spectrum is given in terms of the number of linearly independent square‐summable solutions of the corresponding nonhomogeneous linear system. As a direct consequence, the corresponding results for singular higher‐order symmetric vector difference expressions are given.
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