On the problem of the ergodic constant in the theory of classical Green's functions

In the framework of the theory of classical equilibrium Green's functions, a method is proposed for finding the spectral intensities of the time correlation functions that makes it possible to establish effectively whether or not they have $\delta$-function singularities at $\omega=0$. The spectral intensity of the density–density correlation function is calculated in the mean field approximation as an illustration.