{"paper":{"title":"Universal Taylor Series On Convex Subsets Of $\\Mathbb{C}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Nicholas J. Daras, Vassili Nestoridis","submitted_at":"2013-02-17T19:05:58Z","abstract_excerpt":"We prove the existence of holomorphic functions $f$ defined on any open convex subset ${\\rm \\Omega}\\subset {{\\mathbb C}}^n$, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact set disjoint from $\\bar{{\\rm \\Omega}}$ and on denumerably many convex compact sets in ${{\\mathbb C}}^n\\backslash {\\rm \\Omega}$ which may meet the boundary $\\partial {\\rm \\Omega}$. If the universal approximation is only required on convex compact sets disjoint from $\\bar{{\\rm \\Omega}}$, then $f$ may be chosen to be smooth on $\\partial {\\rm \\Omega}$, that is $f\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4106","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"}