Macroscopical dielectric permittivities of nonhomogeneous media

Based on concepts of the functional analysis and treating the fields E and D as elements of the real vector Hilbert space H , a method is exploited for the calculation of macroscopical permittivities εM of nonhomogeneous media, and bounds within which they acquire their values. Series expansions are obtained for ε M and γ M = ε M –1 , and the convergence conditions are found for the series. Bounds are constructed for ε M , which are contracting with the introduction of additional information on the medium used in the calculation. A comparison with the results of other authors is performed.