On the Maximal Subspaces of Discrete Hamiltonian Systems

In this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester’s inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.