{"paper":{"title":"Functions with ultradifferentiable powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Vincent Thilliez","submitted_at":"2019-08-31T09:36:38Z","abstract_excerpt":"We study the regularity of smooth functions $f$ defined on an open set of $\\mathbb{R}^n$ and such that, for certain integers $p\\geq 2$, the powers $f^p :x\\mapsto (f(x))^p$ belong to a Denjoy-Carleman class $\\mathcal{C}_M$ associated with a suitable weight sequence $M$. Our main result is a statement analogous to a classic theorem of H. Joris on $\\mathcal{C}^\\infty$ functions: if a function $f:\\mathbb{R}\\to\\mathbb{R}$ is such that both functions $f^p$ and $f^q$ with $\\gcd(p,q)=1$ are of class $\\mathcal{C}_M$ on $\\mathbb{R}$, and if the weight sequence $M$ satisfies the so-called moderate growth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00177","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00177/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}