Convolution integral equation

Summary

A convolution integral equation is an integral equation whose kernel depends only on the difference $x - t$ of its two variables. The integral in it is then a convolution of the kernel with the unknown function. Because integral transforms turn convolutions into products, such equations can often be solved explicitly with the Fourier transform or the Laplace transform. They model systems that are invariant under translation, such as linear filters, renewal processes and homogeneous media.