Reconstructing Stieltjes functions from their approximate values: a search for a needle in a hay stack
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Material response of passive media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions – a special class of analytic functions mapping complex upper half-plane into itself. Reconstructing such functions from their experimentally measured values at specific frequencies is one of the central problems that we address in this paper. A definitive reconstruction algorithm that produces a certificate of optimality as well as a graphical representation of the uncertainty of reconstruction is proposed. Its effectiveness is demonstrated in the context of the electrochemical impedance spectroscopy.
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