On the algebra of pseudodifferential operators which is generated by convolutions on the Heisenberg group

Basing on the well-known description for the algebra $\widetilde{\mathfrak{S}_r}$r of the unilateral group convolutions over the Heisenberg group $\mathbb{H}^n$, we portray the algebra of symbols for the algebra $\widetilde{\mathfrak{S}_r}$r that results from expanding the algebra $\widetilde{\mathfrak{S}_r}$, with the operators of multiplication by functions continuous over t he one-point compactification of the Heisenberg group $\mathbb{H}^n$. The decisive instance is in the study of local representations of group convolutions under their localizing over the points of the Heisenberg group.