The Coupling Method for Solving Integral Equations

Abstract

This paper presents a new method to reduce integral operators of various classes to simpler operators, which often are just finite matrices. By this method the problem to find the inverse, generalized inverses, kernel and image of an integral operator is reduced for several cases to the corresponding problem for a finite matrix. The classes of integral operators dealt with include integral operators of the second kind with a finite rank or semi-separable kernel and also, which is more surprising, systems of Wiener-Hopf integral operators and singular integral operators with rational matrix symbols.