Lower bound for the spectrum and the presence of pure point spectrum of a singular discrete Hamiltonian system

In this paper, criteria for limit-point (n) case of a singular discrete Hamiltonian system are established. Furthermore, the lower bound of the essential spectrum is obtained and the present of pure point spectrum is discussed for such system by using the spectral theory of self-adjoint operators in a Hilbert space.  2004 Elsevier Inc. All rights reserved.