In this paper we consider an even-dimensional discrete Hamiltonian system on the set of nonnegative integers in the left-definite form. Using the inertia indices of the hermitian form related with the solutions of the equation we construct some maximal subspaces of the solution space. After constructing some ellipsoids preserving nesting properties we introduce a lower bound for the number of Dirichlet-summable solutions of the equation. Moreover we introduce a limit-point criterion.
