{"paper":{"title":"Bernstein Operators for Extended Chebyshev Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"H. Render, J. M. Aldaz, O. Kounchev","submitted_at":"2008-05-12T11:52:23Z","abstract_excerpt":"Let $U_{n}\\subset C^{n}[ a,b] $ be an extended Chebyshev space of dimension $n+1$. Suppose that $f_{0}\\in U_{n}$ is strictly positive and $% f_{1}\\in U_{n}$ has the property that $f_{1}/f_{0}$ is strictly increasing. We search for conditions ensuring the existence of points $% t_{0},...,t_{n}\\in [ a,b] $ and positive coefficients $\\alpha_{0},...,\\alpha_{n}$ such that for all $f\\in C[ a,b]$, the operator $B_{n}:C[ a,b] \\to U_{n}$ defined by $% B_{n}f=\\sum_{k=0}^{n}f(t_{k}) \\alpha_{k}p_{n,k}$ satisfies $% B_{n}f_{0}=f_{0}$ and $B_{n}f_{1}=f_{1}.$ Here it is assumed that $% p_{n,k},k=0,...,n$, is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1612","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"}