{"paper":{"title":"Smoothing of weights in the Bernstein approximation problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrew Bakan, J\\\"urgen Prestin","submitted_at":"2016-11-21T10:11:48Z","abstract_excerpt":"In 1924 S.Bernstein asked for conditions on a uniformly bounded on $\\mathbb{R}$ Borel function (weight) $w: \\mathbb{R} \\to [0, +\\infty )$ which imply the denseness of algebraic polynomials ${\\mathcal{P} }$ in the seminormed space $ C^{0}_{w} $ defined as the linear set $ \\{f \\in C (\\mathbb{R}) \\ | \\ w (x) f (x) \\to 0 \\ \\mbox{as} \\ {|x| \\to +\\infty}\\}$ equipped with the seminorm $\\|f\\|_{w} := \\sup_{x \\in {\\mathbb{R}}} w(x)| f( x )|$. In 1998 A.Borichev and M.Sodin completely solved this problem for all those weights $w$ for which ${\\mathcal{P} }$ is dense in $ C^{0}_{w} $ but there exists a pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06708","kind":"arxiv","version":2},"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"}