Convolutional systems related with compact non-Abelian groups

The paper describes an approach to determination of convolutional systems specified on a numerical set by redetermining them on objects dual to compact groups. In addition to well-known systems (for which Abelian groups are sufficient) an example is given which permits a version of treating these systems in the case of a numerical semi-infinite set of times (an object dual to the non-Abelian group).