Degenerate kernel

Summary

A degenerate kernel is a kernel that is a finite sum of products $a_i(x) b_i(s)$ of functions of one variable. It is also called a separable kernel or a kernel of finite rank, since its integral operator is a finite-rank operator. An integral equation of the second kind with a degenerate kernel reduces to a finite system of linear equations. Approximating a general kernel by degenerate ones is a main route to Fredholm theory and to numerical methods.