Discrete Equations, Discrete Transformations, and Discrete Boundary Value Problems

Abstract

We study the solvability of discrete elliptic pseudodifferential equations in a sector of the plane. Using special factorization of the symbol, the problem is reduced to a boundary value problem for analytic functions of two variables. A periodic analog of one integral transformation is obtained that was used to construct solutions of elliptic pseudodifferential equations in conical domains. The formula for the general solution of the discrete equation under consideration and some boundary value problems are described in terms of this transformation.