Abstract
A complex response function describing a reaction of a multiโparticle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with nonโnegative imaginary part in the upper halfโplane). Attempts of direct calculations of response functions based on standard approximations of the kinetic theory for real Coulomb condensed systems often result in considerable discrepancies with experiments and computer simulations. At the same time a relatively simple approach using only the exact values of leading asymptotic terms of the response function permits to restrict essentially a subset of Nevanlinna class functions containing this response function, and in this way to obtain sufficient data to explain and predict experimental results. Mathematical details of this approach are demonstrated on an example with the response function being the (external) dynamic electrical conductivity of cold dense hydrogenโlike plasmas. In particular, the exact values of the leading terms of asymptotic expansions of the conductivity are calculated. (ยฉ 2003 WILEYโVCH Verlag GmbH & Co. KGaA, Weinheim)