Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme

The paper deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves. The well‐known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iω E = 0, rot E ‐ iω H = 0, with n × E prescribed on the boundary. The same result holds for the “Mie‐potentials”Which can be proved by a Lemma of Mie [6]. Two numerical examples for the three‐dimensional boundary value problems (field of a dipole, field of reflection) are presented.