Difference potentials and parameterization of solutions of homogeneous difference equations (Q1571291)

The problems of a one-to-one parameterization of the set of solutions to a general homogeneous difference equation are studied by using difference potentials with densities of a special type. On the basis of the concept of a pair of complementary boundary operators, all admissible parameterizations are described. The relation between this problem and the problem of constructing so-called independent internal boundary conditions is analyzed.