Reconstructing Stieltjes functions from their approximate values: a search for a needle in a haystack

Yury Grabovsky

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arXiv · 2101.02775

Reconstructing Stieltjes functions from their approximate values: a search for a needle in a haystack

Yury Grabovsky

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Abstract

Material response of real, passive, linear, time-invariant 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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Yury Grabovsky. 2021-01-07. Reconstructing Stieltjes functions from their approximate values: a search for a needle in a haystack. https://arxiv.org/abs/2101.02775

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