{"paper":{"title":"Optimal Polynomial Admissible Meshes on Some Classes of Compact Subsets of $\\R^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Federico Piazzon","submitted_at":"2013-02-19T19:43:33Z","abstract_excerpt":"We show that any compact subset of $\\R^d$ which is the closure of a bounded star-shaped Lipschitz domain $\\Omega$, such that $\\complement \\Omega$ has positive reach in the sense of Federer, admits an \\emph{optimal AM} (admissible mesh), that is a sequence of polynomial norming sets with optimal cardinality. This extends a recent result of A. Kro\\'o on $\\mathscr C^ 2$ star-shaped domains.\n  Moreover, we prove constructively the existence of an optimal AM for any $K := \\overline\\Omega \\subset \\R^ d$ where $\\Omega$ is a bounded $\\mathscr C^{ 1,1}$ domain. This is done by a particular multivariate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4718","kind":"arxiv","version":6},"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"}