  In the framework of the many-electron s-d exchange model and Hubbard model,
self-consistent equations are derived for the one-particle retarded Green's
function in the many-electron Hubbard X-operator representation. We analyze the
general structure of the single-site approximations and their connection with
the coherent potential approximation (CPA) and dynamic effective field theory
(DMFT). Using the self-consistent approximation, we examine in detail the
picture of the evolution of the electron spectrum with the model parameters
(coupling constants, the concentration of charge carriers). The influence of
various factors (Kondo many-electron scattering, smearing due to damping,
dynamics of localized moment subsystem) on the shape of the density of states
N(E) in the interacting system is investigated. It is shown that the use of the
locator representation allows to avoid in some cases the non-analyticity in
approximate expressions for the Green's functions. Our approach enables one to
reproduce, at certain values of the parameters, three-peak structure of N(E)
near the metal-insulator transition.
