Linear Integrodifferential Equations and the Theory of Reproducing Kernels

Abstract For some general linear integrodifferential equations in the framework of Hubert spaces it will be shown that the theory of reproducing kernels is applicable widely to solve the equations.

1 Introduction

We shall start with a basic idea connecting linear integral transforms in the framework of Hilbert spaces with the theory of reproducing kernels. This basic idea will give, at the same time, a new method to solve the integral equations of Fredholm type of the first kind in the framework of Hilbert spaces, which are fundamental in general linear integral equations.