  The dynamic structure factor is the quantity, which can be measured by means
of Brillouin light-scattering as well as by means of inelastic scattering of
neutrons and X-rays. The spectral (or frequency) moments of the dynamic
structure factor define directly the sum rules of the scattering law. The
theoretical scheme formulated in this study allows one to describe the dynamics
of local density fluctuations in simple liquids and to obtain the expression of
the dynamic structure factor in terms of the spectral moments. The theory
satisfies all the sum rules, and the obtained expression for the dynamic
structure factor yields correct extrapolations into the hydrodynamic limit as
well as into the free-particle dynamics limit. We discuss correspondence of
this theory with the generalized hydrodynamics and with the viscoelastic
models, which are commonly used to analyze the data of inelastic neutron and
X-ray scattering in liquids. In particular, we reveal that the postulated
condition of the viscoelastic model for the memory function can be directly
obtained within the presented theory. The dynamic structure factor of liquid
lithium is computed on the basis of the presented theory, and various features
of the scattering spectra are evaluated. It is found that the theoretical
results are in agreement with inelastic X-ray scattering data.
