Piece-regular solutions of difference equations and difference potentials with density from a jump space

Abstract: General systems of linear difference equations on abstract grids are under consideration. Only the existence and uniqueness of the solution from a given linear space are supposed if the system has an arbitrary right part. The domain of the right part is split into a finite number of disjoint subdomains that leads to corresponding partition of the solution domain into (intersecting) subdomains. A concept of piece-regular solution with some solution of the initial problem in each of these subdomains is defined. A concept of jump of the piece-regular solution is defined too. A potential that in a unique fashion reconstructs each piece-regular solution from its jump is constructed.Note: Research direction:Mathematical problems and theory of numerical method