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Summation methods for Fourier series yielding best order of approximation. (English. Russian original) Zbl 0826.42007
Math. Notes 54, No. 2, 867-871 (1993); translation from Mat. Zametki 54, No. 2, 145-151 (1993).
The author examines the sequence of linear operators $$L_n (f)(x)={1\over\pi}\int^\pi_{- \pi} U_n (t - x) f(t)dt$$, where $$U_n (s) = 1/2 + \sum^n_{k = 1} \lambda_{kn} \cos ks$$, $$n \geq 1$$, on the Banach space $$C_{2 \pi}$$ of continuous $$2 \pi$$-periodic functions. By the method of decomposition of meromorphic functions a sequence $$U_n$$, $$n \geq 1$$, is constructed such that the order of approximation is exact (it is equal to $$1/n^{2m + 2})$$ for each $$2(m + 2)$$-differentiable function $$f$$ with bounded derivate $$f^{(2m + 2)}$$.
##### MSC:
 42A24 Summability and absolute summability of Fourier and trigonometric series
##### Keywords:
summation; Fourier series; order of approximation
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##### References:
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