{"paper":{"title":"Uniform algebras and approximation on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Erlend Forn{\\ae}ss Wold, H{\\aa}kan Samuelsson","submitted_at":"2011-01-25T15:07:15Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{C}^n$ be a bounded domain and let $\\mathcal{A} \\subset \\mathcal{C}(\\bar{\\Omega})$ be a uniform algebra generated by a set $F$ of holomorphic and pluriharmonic functions. Under natural assumptions on $\\Omega$ and $F$ we show that the only obstruction to $\\mathcal{A} = \\mathcal{C}(\\bar{\\Omega})$ is that there is a holomorphic disk $D \\subset \\bar{\\Omega}$ such that all functions in $F$ are holomorphic on $D$, i.e., the only obstruction is the obvious one. This generalizes work by A. Izzo. We also have a generalization of Wermer's maximality theorem to the (distinguish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4840","kind":"arxiv","version":2},"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"}