Discrete double-layer potentials are powerful tools to describe the
solution of discrete Dirichlet problems for the Laplace equation. In
discrete potential theory there are already theorems known, regarding
the existence and uniqueness of the solution of Dirichlet problems. The
results on the solution of these finite difference Dirichlet problems
are based on the single-layer potential. In this paper we extend the
theory by using double-layer potentials.