Towards the theory of group convolution

Let G be a finite group. Following Berman, the general definition of G- spectrum and G-convolution are given which coincide with ordinary definitions if G is an abelian group. Laboriousness estimates of calculations of theoretical-group convolution are found fro non-abelian groups in terms of powers of irreducible representations of such groups. In a number of cases using this construction permits to obtain a gain in time for certain lengths of convolution signals.