This generalizes to convolution in an arbitrary group (and even groupoid, and even category), not necessarily one that is commutative like the reals or integers

This generalizes to convolution in an arbitrary group (and even groupoid, and even category), not necessarily one that is commutative like the reals or integers are. For group convolution over a group G, the functions take values in the complex numbers and have domain the elements of G. The value of the convolution of two such functions f and g at a point c (a group element) is computed by taking the sums f(a)*g(b) where ab = c. This has applications in quantum mechanics where non-commutativity plays a prominent role.