General Wiener-Hopf factorization of matrix kernels with exponential phase factors

The factorization of Wiener-Hopf matrices with exponentially growing elements has long remained an unsolved problem. Such matrices often occur in the calculation of scattering from complex canonical geometries and other problems in mathematical physics. Here a general method is given for resolving the difficulty and obtaining a single scalar integral equation, the solution of which generates the required factors. It is proven that this solution has a simple infinite series representation. The method is illustrated by reference to three particular examples. The first is a model matrix arising from a system of simple delay-differential equations and the second occurs in the diffraction of sound by two 'knife-edges.' Finally a heat conduction problem is solved for an infinite wedge with asymmetric mixed boundary conditions on its faces.