Fredholm equations for non-symmetric kernels, with applications to iterated integral operators

Abstract

We give the Jordan form and the Singular Value Decomposition for an integral operator $\mathcal{N}$ with a non-symmetric kernel $N(y,z)$. This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the behaviour of ${\mathcal{N}}^n$ and $(\mathcal{N}{\mathcal{N}}^{\ast }{)}^n$ for large $n$.

12 A4 pages