Discrete Potential and its Properties I (A. NATURAL SCIENCE)

We expand properties about the discrete potential theory. The lattice functions, take the values only at the lattice points of the N-dimensional Euclidean space R^N (N≧2), defined on the lattice (set of lattice points) X have analogous behavior for continuous functions under certain conditions, still more are closely connected with harmonic- and superharmonic-functions, Green's functions and potentials etc. In this paper we investigate the representation of a solution of the Dirichlet problem and properties of Green's functions.departmental bulletin pape