{"paper":{"title":"Pad\\'{e} Approximants, density of rational functions in $\\bbb{A^\\infty(\\OO)}$ and smoothness of the integration operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ilias Zadik, Vassili Nestoridis","submitted_at":"2012-12-18T15:44:10Z","abstract_excerpt":"First we establish some generic universalities for Pad\\'{e} approximants in the closure $X^\\infty(\\OO)$ in $A^\\infty(\\OO)$ of all rational functions with poles off $\\oO$, the closure taken in $\\C$ of the domain $\\OO\\subset\\C$.\\ Next we give sufficient conditions on $\\OO$ so that $X^\\infty(\\OO)=A^\\infty(\\OO)$.\\ Some of these conditions imply that, even if the boundary $\\partial\\OO$ of a Jordan domain $\\OO$ has infinite length, the integration operator on $\\OO$ preserves $H^\\infty(\\OO)$ and $A(\\OO)$ as well.\\ We also give an example of a Jordan domain $\\OO$ and a function $f\\in A(\\OO)$, such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4394","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":""},"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"}