{"paper":{"title":"Weighted-$L^2$ polynomial approximation in $\\mathbb{C}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"John Erik Forn{\\ae}ss, Jujie Wu, S\\'everine Biard","submitted_at":"2018-05-30T00:22:30Z","abstract_excerpt":"We study the density of polynomials in $H^2(\\Omega,e^{-\\varphi})$, the space of square integrable holomorphic functions in a bounded domain $\\Omega$ in $\\mathbb{C}$, where $\\varphi$ is a subharmonic function. In particular, we prove that the density holds in Carath\\'{e}odory domains for any subharmonic function $\\varphi$ in a neighborhood of $\\overline{\\Omega}$. In non-Carath\\'{e}odory domains, we prove that the density depends on the weight function, giving examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11756","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"}