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Approximation of functions of several variables by Féjer sums. (English. Russian original) Zbl 0557.42004
Math. Notes 36, 553-564 (1984); translation from Mat. Zametki 36, No. 1, 123-136 (1984).
The author proves three theorems about behaviour of the quantity \(\rho_{R,s}(X^ m_{\epsilon},D)=\sup \{\| f- \sigma_{R,s}(f;D)\|_{X^ m}:f\in X^ m_{\epsilon}\},\) where \(X^ m_{\epsilon}=\{f\in X^ m:E_ r(f)_{X^ m}\leq \epsilon_ r(r\geq 0)\},\) \(E_ r(f)_{X^ m}\) is the best approximation, \(\sigma_{R,s}\) is the de la (Vallée-Poussin means. The paper includes a comprehensive list of references with 18 entries).
Reviewer: R.Gajewski
MSC:
42B05 Fourier series and coefficients in several variables
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