On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces

Let D subset of R-3 be a bounded domain with connected boundary partial der ivativeD of class C-2. It is shown that Herglotz wave functions are dense i n the space of solutions to the Helmholtz equation with respect to the norm in H-1(D) and that the electric fields of electromagnetic Herglotz pairs a re dense in the space of solutions to curl curl E = k(2)E with respect to t he norm in H-curl(D). Two proofs are given in each case, one based on the d enseness of the traces of Herglotz wave functions on partial derivativeD an d the other on variational methods. Copyright (C) 2001 John Wiley & Sons, L td.