Reconstruction of the density of states from its moments

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Abstract
The problem of the reconstruction of a non-negative spectral density from its low-order power moments is reexamined. With the assumption that the parameters of the continued-fraction representation of the Green's function obey a certain analytic expression, we derive an extrapolation procedure for them. This procedure leads to significantly improved results and is simple to implement. Several relevant examples of its application are provided and show the advantages of our method, which works adequately both for the translationally invariant case (i.e., when Van Hove singularities are present) and also in the general disordered situation. The method is particularly useful in trying to estimate the position of the effective band edges (Lifshitz limits), for which it yields quite accurate values.