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- Bernstein's_theorem_(approximation_theory) 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.".
- Bernstein's_theorem_(approximation_theory) wikiPageID "32140327".
- Bernstein's_theorem_(approximation_theory) wikiPageRevisionID "467329258".
- Bernstein's_theorem_(approximation_theory) hasPhotoCollection Bernstein's_theorem_(approximation_theory).
- Bernstein's_theorem_(approximation_theory) subject Category:Approximation_theory.
- Bernstein's_theorem_(approximation_theory) subject Category:Theorems_in_approximation_theory.
- Bernstein's_theorem_(approximation_theory) type Abstraction100002137.
- Bernstein's_theorem_(approximation_theory) type Communication100033020.
- Bernstein's_theorem_(approximation_theory) type Message106598915.
- Bernstein's_theorem_(approximation_theory) type Proposition106750804.
- Bernstein's_theorem_(approximation_theory) type Statement106722453.
- Bernstein's_theorem_(approximation_theory) type Theorem106752293.
- Bernstein's_theorem_(approximation_theory) type TheoremsInApproximationTheory.
- Bernstein's_theorem_(approximation_theory) 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.".
- Bernstein's_theorem_(approximation_theory) label "Bernstein's theorem (approximation theory)".
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- Bernstein's_theorem_(approximation_theory) sameAs Q4894565.
- Bernstein's_theorem_(approximation_theory) sameAs Bernstein's_theorem_(approximation_theory).
- Bernstein's_theorem_(approximation_theory) wasDerivedFrom Bernstein's_theorem_(approximation_theory)?oldid=467329258.
- Bernstein's_theorem_(approximation_theory) isPrimaryTopicOf Bernstein's_theorem_(approximation_theory).