Difference kernel

Summary

A difference kernel is a kernel of the form $K(x, s) = k(x - s)$, which depends only on the difference of its two variables. Its integral operator is a convolution with $k$, so it commutes with translations. Integral equations with difference kernels are called convolution equations. Transforms that turn convolutions into products, such as the Laplace transform and the Fourier transform, reduce them to algebraic equations.