The Classical Moment Problem and the Calculation of Thermal Averages

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Abstract
The physical information contained in the first 2n moments of the single-particle spectral weight function of a fermionic many-body system is investigated. The approach is based on the mathematical theory of the classical moment problem. Under consideration are the thermal as well as dynamical properties of the system. Using this information, approximate n-pole single-particle thermal Green's functions and the corresponding spectral weight functions are constructed. It is shown that these approximations are not unique and depend on a real parameter. This dependence is used for the calculation of the rigorous error bounds of the approximate thermal averages.