Convolution of functions on $\RR^n$

Let \(f,g\colon\RR^n\to\CC\) be measurable. The convolution of \(f\) and \(g\) is the function \[ (f * g)(x) \coloneqq \int_{\RR^n} f(x-y)\, g(y) \, dy, \] defined at every \(x\in\RR^n\) for which the integral converges absolutely.