Approximation of a class of singular integrals by algebraic polynomials with regard to the location of a point on an interval (Q2783081)
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scientific article; zbMATH DE number 1729330
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of a class of singular integrals by algebraic polynomials with regard to the location of a point on an interval |
scientific article; zbMATH DE number 1729330 |
Statements
19 February 2003
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Nikolski-Timan type theorem
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Achiezer-Krein constants
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Sobolev-Hölder class
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Approximation of a class of singular integrals by algebraic polynomials with regard to the location of a point on an interval (English)
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The author proves a sharp version of a S. Nikolskij-A. Timan type result for the class NEWLINENEWLINENEWLINE\(W^r_\infty H^\omega[-1,1]\) of \(r\)-differentiable functions satisfying NEWLINE\[NEWLINE|f^{(r)}(x)- f^{(r)}(y)|\leq \omega(|x- y|).NEWLINE\]NEWLINE Here \(\omega\) is assumed to be concave and such that \(\omega(0)= 0\) and \(t\omega'(t)\) is nondecreasing.NEWLINENEWLINEFor the entire collection see [Zbl 0981.00017].
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