Über Grundlösungen von Differenzenoperatoren (Q794406)

The paper considers difference equations which arise from linear partial differential equations with constant coefficients by its discretization as functional equations in certain spaces of distributions. Applying the Fourier transformation it is constructively shown that such equations possess fundamental solutions in a neighbourhood (with respect to the discretization parameter) of the fundamental solution of the corresponding differential equation. There is a full analogy in handling difference and differential problems. An initial-value problem for the one-dimensional equation of heat conduction as one example for an useful application of discrete fundamental solutions is added.