On the Factorization of Certain Kernels Arising in Functional Equations of the Wiener-Hopf Type

Abstract

The Wiener-Hopf technique is one of the most powerful methods for analyzing the scattering and diffraction problems of electromagnetic or acoustic waves. The essential step for the solution contains the so-called factorization. This procedure needs to split certain analytic functions (kernels) into the multiplication form of two functions which have semi-infinite regions of regularity. In this paper, factorization of typical kernel functions which arise in the Wiener-Hopf equations concerned with dielectric objects, is discussed. By applying a general factorization theorem, exact integral representations of split functions are obtained and then some approximate formulas are derived via rigorous asymptotic procedure. As a result, it is pointed out that final approximate formulas are useful for high frequency range.