Difference Potentials and Generalized Poincare-Steklov Operators for Difference Boundary-Value Problems

In this preprint we investigate connection between boundary problems for general linear systems of difference equations and Ryaben'kii's difference potentials and boundary projections. A concept of complementary boundary value operators is introduced and, bearing on it, a class of so called generalized difference Poincare-Steklov operators is characterized for difference systems of considered type. Representation of the action of generalized Poincare-Steklov is obtained in terms of boundary projections and operators of boundary conditions for some well-posed difference boundary-value problems.