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 derivativeD of class C-2. It is shown that Herglotz wave functions are dense in 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 are dense in the space of solutions to curl curl E = k(2)E with respect to the norm in H-curl(D). Two proofs are given in each case, one based on the denseness of the traces of Herglotz wave functions on partial derivativeD and the other on variational methods. Copyright (C) 2001 John Wiley & Sons, Ltd.