{"paper":{"title":"Orthogonal polynomials for area-type measures and image recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"E. B. Saff, H. Stahl, N. Stylianopoulos, V. Totik","submitted_at":"2014-03-25T19:07:28Z","abstract_excerpt":"Let $G$ be a finite union of disjoint and bounded Jordan domains in the complex plane, let $\\mathcal{K}$ be a compact subset of $G$ and consider the set $G^\\star$ obtained from $G$ by removing $\\mathcal{K}$; i.e., $G^\\star:=G\\setminus \\mathcal{K}$. We refer to $G$ as an archipelago and $G^\\star$ as an archipelago with lakes. Denote by $\\{p_n(G,z)\\}_{n=0}^\\infty$ and $\\{p_n(G^\\star,z)\\}_{n=0}^\\infty$, the sequences of the Bergman polynomials associated with $G$ and $G^\\star$, respectively; that is, the orthonormal polynomials with respect to the area measure on $G$ and $G^\\star$. The purpose of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6456","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"}