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After recalling the definition and properties of one-body time-ordered Green\u2019s functions and self-energies, and the mathematical structure of the Hubbard and Anderson impurity models, we describe the specific\n                    <jats:italic>impurity solver<\/jats:italic>\n                    we have studied in this article, namely the Iterated Perturbation Theory (IPT) solver, which can be conveniently formulated using Matsubara\u2019s Green\u2019s functions.\n                  <\/jats:p>","DOI":"10.1007\/s00220-026-05647-9","type":"journal-article","created":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T18:11:37Z","timestamp":1780769497000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Mathematical Analysis of IPT-DMFT"],"prefix":"10.1007","volume":"407","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8876-8254","authenticated-orcid":false,"given":"Eric","family":"Canc\u00e8s","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alfred","family":"Kirsch","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Solal","family":"Perrin-Roussel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,6]]},"reference":[{"issue":"2","key":"5647_CR1","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1307\/mmj\/1029002212","volume":"26","author":"MB Abrahamse","year":"1979","unstructured":"Abrahamse, M.B.: The Pick interpolation theorem for finitely connected domains. 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