The basic functionsb andh for Fredholm integral equations with displacement kernels

Abstract

In many branches of applied mathematics, including lateral inhibition in neural systems, radiation dosimetry, and optimal filtering of noisy signals, important roles are played by Fredholm integral equations with displacement kernels. Frequently, certain functionals on the solutions of the integral equations are as important as the solutions themselves. In this paper, it is shown that many such functionals may be expressedalgebraically in terms of two basic functions,b andh, and that these functions themselves are solutions of a certain Cauchy system and a system of singular integral equations.