Convolution $(f\ast g)(\xi) = \int f(\xi - y)g(y) \, dy$

Let \(f, g\colon\RR^n\to\CC\) be measurable. At every \(\xi\in\RR^n\) for which the integral converges absolutely, the convolution of \(f\) and \(g\) is \[ (f\ast g)(\xi) = \int_{\RR^n} f(\xi - y)g(y) \, dy. \]