Iterated kernel

Summary

The iterated kernels of a kernel $K$ are the kernels $K_1 = K$, $K_2$, $K_3$, ... of the powers of its integral operator. They are defined by $K_{n}(x, s) = \int_a^b K(x, t) K_{n-1}(t, s) \, dt$, the continuous analogue of matrix powers. They are the terms of the Liouville–Neumann series and of the resolvent kernel. Their growth in $n$ decides for which $\lambda$ these series converge.