Strong limit point criteria for a class of singular discrete linear Hamiltonian systems (Q2644013)

This article deals with the discrete linear Hamiltonian system \[ \Delta y(t) = (\lambda W(t)+P(t))R(y)(t), \quad t\in\mathbb{N}_0^+, \] where \(\Delta\) is the forward difference operator and \(W(t) = \text{diag}\{W_1(t),W_2(t)\}\) is the weight function with nonnegative definite matrices \(W_1(t)\) and \(W_2(t)\) of same dimension; \(P(t)\) is a Hermitian matrix, and the partial right shift operator fulfills \(R(y)(t) = (x^T(t+1),u^T(t))^T\) with \(y(t) = (x^T(t),y^T(t))\). The authors distinguish between the strong limit point case and the weak limit point case, and they formulate sufficient conditions for the strong limit point case. Furthermore, a second-order formally self-adjoint vector difference equation is analyzed, which is related to the above Hamiltonian system, and two further criteria for the strong limit point case are obtained.