Group Convolution

The convolution of two Complex-valued functions on a Group $G$ is defined as

$$(a*b)(g) = \sum_{k\in G} a(k)b(k^{-1} g)$$

where the Support (set which is not zero) of each function is finite.

References

Weinstein, A. ``Groupoids: Unifying Internal and External Symmetry.'' Not. Amer. Math. Soc. 43, 744-752, 1996.