Communicated by E. Meister
This paper deals with a famous diffraction problem for a single half-plane : x'0, y"0 as an obstacle and for some time-harmonic plane incident wave field. Rawlins in 1975 was the first to solve the mixed (Dirichlet/Neumann) boundary value problem for the scalar Helmholtz equation. He also was the first to solve the equivalent pair of coupled Wiener-Hopf equations explicitly by factoring their discontinuous 2;2 Fourier matrix symbol in 1980. Although for real wave numbers k the usual factorization procedure fails it will serve as the basis: Following the lines given by Ali Mehmeti in his habilitation thesis [1] for the (Dirichlet/Dirichlet) boundary value problem we combine the idea of integral path deforming along the branch cuts of the characteristic square root (( !k) given in Meister's book [13] with the modern Wiener-Hopf method solution derived by Speck [24] explicitly in a H>C, *0, Sobolev space setting. The symmetry of the intermediate spaces HQ, H\Q, "s"( , which is due to generalized factorization, plays a key role in deforming the Fourier integral paths in order to get Laplace transform representations of the generalized eigenfunctions of the problem. As a remarkable fact 0( ( must hold here. 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.