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

We give the Jordan form and the singular value decomposition for an integral operator NN with a non-symmetric kernel N(y,z)N(y,z). This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the behaviour of NnNn and (NN∗)n(NN∗)n for large n.