Matrix Wiener-Hopf factorisation

Abstract

A direct method is described for effecting the explicit Wiener-Hopf factorisation of a class of (2 x 2)-matrices. The class is determined such that the factorisation problem can be reduced to a matrix Hilbert problem which involves an upper or lower triangular matrix. Then the matrix Hilbert problem can be further reduced to three scalar Hilbert problems on a half-line, which are solvable in the standard manner. The factorisation technique is applied to the matrices that arise from two problems in diffraction theory, thus permitting these diffraction problems to be solved in closed form (at least in principle).