Zakharov’s transformation in the problem of galaxy mass distribution function

Owing to non-locality [Balk et al., Zh. Exp. Teor. Fiz. (Sov. Phys. JETP) 98 (1990) 446] of galaxy mass spectrum formed by mergings the additional approximate conservation law affects its intermediate asymptotics power index which proves to be intervening between the constant mass flux and that of the number of massive galaxies. Analytical description of this asymptotics, which essentially uses the Smoluchowsky kinetic equation symmetry transformation is presented. The result is compared with the recently discovered steepness of galaxy luminosity function on its faint edge. The problem of distribution of the main part of barionic mass is briefly discussed in this context.