{"paper":{"title":"Sets of uniqueness for uniform limits of polynomials in several complex variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"K. Makridis, V. Nestoridis","submitted_at":"2013-04-19T19:28:05Z","abstract_excerpt":"We investigate the sets of uniform limits $A(\\bar{B}_n)$, $A(\\bar{D}^I)$ of polynomials on the closed unit ball $\\bar{B}_n$ of $\\mathbb{C}^n$ and on the cartesian product $\\bar{D}^I$ where $I$ is an arbitrary set and $\\bar{D}$ is the closed unit disc in $\\mathbb{C}$. We introduce the notion of set of uniqueness for $A(\\bar{D}^I)$ (respectively for $A(\\bar{B}_n)$) for compact subsets $K$ of $T^I$ (respectively of $\\partial \\bar{B}_n$) where $T=\\partial D$ is the unit circle. Our main result is that if $K$ has positive measure then $K$ is a set of uniqueness. The converse does not hold. Finally,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5511","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"}