{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/reconstructing-stieltjes-functions-from-their","title":"Reconstructing Stieltjes functions from their approximate values: a search for a needle in a haystack","arxiv_id":"2101.02775","date":"2021-01-07","proceeding":null,"authors":["Yury Grabovsky"],"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.","url_abs":"https://arxiv.org/abs/2101.02775v5","url_pdf":"https://arxiv.org/pdf/2101.02775v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"reconstructing-stieltjes-functions-from-their","repo_url":"https://github.com/yurygrabovsky/stieltjes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}