Continuous kernel

Summary

A continuous kernel is a kernel $K(x, s)$ that is a continuous function of both variables on a closed bounded square $[a, b] \times [a, b]$. It is the setting of the classical theory of Fredholm and Volterra. The integral operator with a continuous kernel maps continuous functions to continuous functions and is a compact operator on the space of continuous functions. Iteration methods, the Liouville–Neumann series and the Fredholm determinant are first developed for such kernels.