A generalized approach to solving Fredholm and Wiener-Hopf integral equations

Abstract

A generalized method is presented for the solution of Fredholm and Wiener-Hopf integral equations using the theory of distributions. By separating the integral through determination of the limits of integration, bounded linear differential operators may be defined which reduce the integral equation problem to one of solving a distributional differential equation. These operators may then be combined to give an equation defining the desired unknown function. This method has the advantage that it is applicable to equations which contain nonstationary kernels or stationary rational or nonrational kernels independent of any assumption concerning separability of the kernel. The only assumption made is that the operators exist. The technique is applied to some specific problems and the results are shown to be the same as those obtained by other authors.