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

Owing to non-locality [Balk et al., Zh. Exp. Teor. Fit. (Sov. Phys. JETP) 9 8 (1990) 446] of galaxy mass spectrum formed by mergings the additional app roximate conservation law affects its intermediate asymptotics power index which proves to be intervening between the constant mass flux and that of t he number of massive galaxies. Analytical description of this asymptotics, which essentially uses the Smoluchowsky kinetic equation symmetry transform ation is presented. The result is compared with the recently discovered ste epness of galaxy luminosity function on its faint edge. The problem of dist ribution of the main part of barionic mass is briefly discussed in this con text. (C) 2001 Elsevier Science B.V. All rights reserved.