{"paper":{"title":"Best polynomial approximation on the triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Christian Krattenthaler, Han Feng, Yuan Xu","submitted_at":"2017-11-13T18:49:19Z","abstract_excerpt":"Let $E_n(f)_{\\alpha,\\beta,\\gamma}$ denote the error of best approximation by polynomials of degree at most $n$ in the space $L^2(\\varpi_{\\alpha,\\beta,\\gamma})$ on the triangle $\\{(x,y): x, y \\ge 0, x+y \\le 1\\}$, where $\\varpi_{\\alpha,\\beta,\\gamma}(x,y) := x^\\alpha y ^\\beta (1-x-y)^\\gamma$ for $\\alpha,\\beta,\\gamma > -1$. Our main result gives a sharp estimate of $E_n(f)_{\\alpha,\\beta,\\gamma}$ in terms of the error of best approximation for higher order derivatives of $f$ in appropriate Sobolev spaces. The result also leads to a characterization of $E_n(f)_{\\alpha,\\beta,\\gamma}$ by a weighted $K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04756","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"}