On Discrete Boundary Value Problems

We consider discrete pseudo-differential equations and related discrete boundary value problems in appropriate discrete spaces. First we study simplest types of operators acting in canonical domains like a half-space and a cone. We try to describe solvability conditions for such equations and boundary value problems and further to compare the discrete and continue cases. We use a concept of periodic factorization for elliptic symbols to obtain a form of solution for such equations in canonical domains.