Geodesic
On the Order of Approximation by Riesz Means in Multiplicative Systems in the Classes~$E_X[\varepsilon]$
Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 508-523

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We establish the order of approximation by Riesz means of the Fourier series in a multiplicative system of a class of functions with given majorant of the sequence of best approximations. In some cases, approximations by Riesz means and best approximations are considered in a specific space, but, in other cases, approximations by Riesz means are considered in spaces with a stronger norm.
Keywords: Riesz mean, approximation by Riesz means, Fourier series, multiplicative system, Vilenkin system, Dirichlet kernel, Hardy space.
Mots-clés : Fejér kernel 
@article{MZM_2011_89_4_a3,
     author = {T. V. Iofina},
     title = {On the {Order} of {Approximation} by {Riesz} {Means} in {Multiplicative} {Systems} in the {Classes~}$E_X[\varepsilon]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {508--523},
     publisher = {mathdoc},
     volume = {89},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a3/}
}
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T. V. Iofina. On the Order of Approximation by Riesz Means in Multiplicative Systems in the Classes~$E_X[\varepsilon]$. Matematičeskie zametki, Tome 89 (2011) no. 4, pp. 508-523. http://geodesic.mathdoc.fr/item/MZM_2011_89_4_a3/