On the solutions of generalized discrete Poisson equation (Q1014454)

For a generalized discrete Poisson equation in \(d\) dimensions it is shown that the solution with square-summable discrete derivatives is unique up to a constant. Furthermore, a necessary and sufficient condition for the existence of finite solutions is given. Additionally, a necessary condition for the existence of solutions with square-summable differences is derived. It is shown that this condition is, in general, not sufficient.