The Wiener–Hopf–Hilbert method for diffraction problems

A powerful method of solving diffraction problems is described. In it, a system of Wiener–Hopf equations is transformed into a system of Hilbert problems. The latter apparently can be solved fora wider range of problems than the former. As an example, the diffraction problem of a plane wave incident on a half-plane with different face impedances is considered. This problem is not solvable by ordinary Wiener–Hopf techniques, but yields to the new method. Possible applications to some unsolved problems are mentioned.