Frequency moments analysis of the dynamic structure factor of statistical systems

General relations of the theory of classical moments and orthogonal polynomials are applied to the construction of approximate expressions for the dynamic structure factor of statistical systems. With the help of the Nevanlinna theorem the respective expressions which interpolate the dynamic scattering function are constructed in terms of the static structure factor and a set of moments which are considered to be given because of their connection with spectral line shape parameters (integral intensitivity of scattering; shift, dispersion and asymmetry of spectral line, etc.). The efficiency of choice of respective interpolational expressions is proposed to be controlled self-consistently with the help of appropriate Tchebycheff–Markov inequalities. The correct limiting transitions to well-known results obtained within the memory function formalism are demonstrated. The possible application of the given approach to studying critical dynamic light scattering data, is demonstrated.