Approximation of periodic functions in the classes \(H_q^\Omega\) by linear methods (Q2884659)
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scientific article; zbMATH DE number 6039343
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of periodic functions in the classes \(H_q^\Omega\) by linear methods |
scientific article; zbMATH DE number 6039343 |
Statements
30 May 2012
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modulus of continuity
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linear approximations
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Bernstein's inequality
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Nikolskii's inequality
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functions of several variables
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Approximation of periodic functions in the classes \(H_q^\Omega\) by linear methods (English)
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It has been shown that, if approximation in norm of \(L_\infty\) (or \(H_1\)) of functions in the classes \(H_\infty^\Omega\) (in \(H_1^\Omega\), respectively) by some linear operators have the same order of magnitude as the best approximation, then the set of norms of these operators is unbounded. Also Bernstein's and the Jackson-Nikolskii's inequalities are proved for trigonometric polynomials with spectra in the sets \(Q(N)\) (in \(T(N,\Omega)\)).
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