Abstract
Green functions, being the basic entities of a great part of condensed
matter theory, are 'Herglotz', i.e. they can be analytically continued
into the open half-planes forming the physical sheet of complex energy.
On the real-energy axis they are usually nonanalytic and may even
be distributions, which makes their numerical calculation there hard
to perform. On the contrary, being smooth functions in the complex
plane, they may easily be computed numerically there, provided closed
formal expressions are given. The problem of a numerical analytical
continuation towards the singularities (deconvolution) has been treated
rather empirically in recent literature. Here a systematic analysis
of the extrapolation error propagation is given, and an optimised
deconvolution procedure is proposed. The focus is on the spectral
function, the density of states and integrated density of states
problems. Examples are given demonstrating the power of the procedure.
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