Definition 1

Let $G$ be a Lie group, $g$ and $g'$ two points of $G$ and let $t \in T_g^{(\infty)}(G)$ $t' \in T_{g'}^{(\infty)}(G)$ be two point distributions at $g$ and $g'$ on $G$ (Differentiable and Analytic Manifolds*, R, 13.2.1). The convolution product of $t$ and $t'$, denoted by $t * t'$, is the image of $t \otimes t'$ under the mapping $(h, h') \mapsto hh'$ of $G \times G$ into $G$ (Differentiable and Analytic Manifolds, R, 13.2.3).*