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We give the Jordan form and the Singular Value Decomposition for an integraloperator ${\cal N}$ with a non-symmetric kernel $N(y,z)$. This is used to givesolutions of Fredholm equations for non-symmetric kernels, and to determine thebehaviour of ${\cal N}^n$ and $({\cal N}{\cal N^*})^n$ for large $n$.

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