Fredholm Theory for Integral Equations with Symmetric Kernels

Abstract

In this study, integral equations with symmetric kernels are discussed. By creating an orthonormal eigen function system containing a symmetric kernel, the corresponding differential equation will be discussed. If the eigen system of a symmetric kernel is known, it becomes easier to examine the symmetric Fredholm equation of the first kind. We also prove the existence of an eigenvalue if K is a symmetric and everywhere continuous operator, and that a symmetric kernel produces a completely continuous operator. Finding the eigenvalue with both methods will be shown.