A Generalized Function-Theoretic Technique for the Solution of Some Diffraction Problems

Abstract

A straightforward approach to the solution of a general class of Wiener-Hopf equations is developed. The advantage of the present procedure is to apply the topological concept so that a rather difficult step of performing factorization in the usual procedure can be avoided. A new theorem regarding additive decomposition is deduced and verified in some detail; a theorem of approximating a function in a topological space is presented; in addition, an alternative view of Laplace transformation is given. The solutions of two typical diffraction problems are used to demonstrate the method; moreover application of the concept of a generalized operator to simplity problem formulation is well illustrated.