Binary operations in the set of solutions of a partial difference equation

Abstract:

Let $\mathcal {P}$ be a partial difference operator with constant coefficients in n independent (discrete) variables, and let ${\mathcal {S}_\mathcal {P}} = \{ f:{Z^n} \to {\mathbf {C}};\mathcal {P}f = 0\}$. We introduce a certain class of binary operations ${\mathcal {S}_\mathcal {P}} \times {\mathcal {S}_\mathcal {P}} \to {\mathcal {S}_\mathcal {P}}$ generalizing a binary operation introduced by Duffin and Rohrer.