Bernstein's theorem (approximation theory)
id:
bernstein-s-theorem-approximation-theory-279-4236496
title:
Bernstein's theorem (approximation theory)
text:
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 conti
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encyclopedia
description:
In approximation theory, a converse to Jackson's theorem
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https://en.wikipedia.org/wiki/Bernstein%27s_theorem_(approximation_theory)
date created:
date modified:
2023-04-17T09:35:55Z
main entity:
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