{"paper":{"title":"Composition in ultradifferentiable classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Armin Rainer, Gerhard Schindl","submitted_at":"2012-10-18T11:44:36Z","abstract_excerpt":"We characterize stability under composition of ultradifferentiable classes defined by weight sequences $M$, by weight functions $\\omega$, and, more generally, by weight matrices $\\mathfrak{M}$, and investigate continuity of composition $(g,f) \\mapsto f \\circ g$. In addition, we represent the Beurling space $\\mathcal{E}^{(\\omega)}$ and the Roumieu space $\\mathcal{E}^{\\{\\omega\\}}$ as intersection and union of spaces $\\mathcal{E}^{(M)}$ and $\\mathcal{E}^{\\{M\\}}$ for associated weight sequences, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5102","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}