Best \(L^ 1\)-approximation by polynomials. II (Q805950)
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scientific article; zbMATH DE number 4205052
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Best \(L^ 1\)-approximation by polynomials. II |
scientific article; zbMATH DE number 4205052 |
Statements
Best \(L^ 1\)-approximation by polynomials. II (English)
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1990
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The paper is the continuation of [\textit{H. Fiedler}, \textit{W. B. Jurkat}, J. Approximation Theory 37, 269-292 (1983; Zbl 0526.41011)]. It is given the bound from above of the difference between the value of best \(L^ 1\)-approximation of \(f\in C^ n[-1;1]\) \((f^{(n)}(x)\geq 0\) for \(| x| \leq \delta \leq 1)\) by real polynomials of degree not exceeding n and doubled nth coefficient of Fourier series expansion of f by Chebyshev polynomials of second kind.
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Markov class of functions
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coefficients of Fourier-Chebyshev expansions
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best \(L^ 1\)-approximation
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Chebyshev polynomials
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