{"paper":{"title":"Norm preserving extensions of bounded holomorphic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"John McCarthy, Lukasz Kosinski","submitted_at":"2017-04-12T17:46:04Z","abstract_excerpt":"A relatively polynomially convex subset $V$ of a domain $\\Omega$ has the extension property if for every polynomial $p$ there is a bounded holomorphic function $\\phi$ on $\\Omega$ that agrees with $p$ on $V$ and whose $H^\\infty$ norm on $\\Omega$ equals the sup-norm of $p$ on $V$. We show that if $\\Omega$ is either strictly convex or strongly linearly convex in ${\\mathbb C}^2$, or the ball in any dimension, then the only sets that have the extension property are retracts. If $\\Omega$ is strongly linearly convex in any dimension and $V$ has the extension property, we show that $V$ is a totally ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03857","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"}