  The analytical method of solving the boundary problems for a system of
equations describing the behaviour of electrons and an electric field in the
Maxwell plasma half-space is developed. Here the diffusion reflection of
electrons from the surface as a boundary condition is supposed. The exact
solution for boundary value problem of the Vlasov-Maxwell equations through the
eigenfunctions of the discrete spectrum and the continuous spectrum is
obtained. The method of decomposition by eigenfunctions of discrete and
continuous spectrum is used. The exact expression for the surface impedance
also is obtained.
