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Statements

Subject Item: dbr:List_of_eponyms_(A–K)
dbo:wikiPageWikiLink: dbr:Bernstein's_theorem_(approximation_theory)

Subject Item: dbr:Lethargy_theorem
dbo:wikiPageWikiLink: dbr:Bernstein's_theorem_(approximation_theory)

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dbo:wikiPageWikiLink: dbr:Bernstein's_theorem_(approximation_theory)

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dbo:wikiPageWikiLink: dbr:Bernstein's_theorem_(approximation_theory)

Subject Item: dbr:Bernstein's_theorem_(approximation_theory)
rdf:type: yago:Theorem106752293 yago:Abstraction100002137 yago:Message106598915 yago:Statement106722453 yago:Proposition106750804 yago:Communication100033020 yago:WikicatTheoremsInApproximationTheory
rdfs:label: Bernstein's theorem (approximation theory)
rdfs:comment: In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912. For approximation by trigonometric polynomials, the result is as follows: Let f: [0, 2π] → C be a 2π-periodic function, and assume r is a natural number, and 0 < α < 1. If there exists a number C(f) > 0 and a sequence of trigonometric polynomials {Pn}n ≥ n0 such that then f = Pn0 + φ, where φ has a bounded r-th derivative which is α-Hölder continuous.
dcterms:subject: dbc:Theorems_in_approximation_theory
dbo:wikiPageID: 32140327
dbo:wikiPageRevisionID: 618549696
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dbo:abstract: In approximation theory, Bernstein's theorem is a converse to Jackson's theorem. The first results of this type were proved by Sergei Bernstein in 1912. For approximation by trigonometric polynomials, the result is as follows: Let f: [0, 2π] → C be a 2π-periodic function, and assume r is a natural number, and 0 < α < 1. If there exists a number C(f) > 0 and a sequence of trigonometric polynomials {Pn}n ≥ n0 such that then f = Pn0 + φ, where φ has a bounded r-th derivative which is α-Hölder continuous.
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Subject Item: dbr:Jackson's_inequality
dbo:wikiPageWikiLink: dbr:Bernstein's_theorem_(approximation_theory)

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