Simultaneous Wiener-Hopf Equations and Their Application to Diffraction Problems in Electromagnetic Theory

Abstract

Simultaneous Wiener-Hopf equations with the kernel which is a symmetric and normal Jacobi matrix and their application to diffraction problems in electromagnetic theory are discussed. It can be shown that there exists a constant orthogonal matrix such that it transforms the kernel into a diagonal form, so the standard Wiener-Hopf procedure can be applied to solve the n simultaneous equations exactly. On the basis of this result, a treatment is made of the problem of a duct with n semi-infinite parallel plates. Under appropriate conditions a rigorous solution is obtained by an elementary method without recourse to Sylvester’s theorem.