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 Mat. Zametki, 2011, Volume 89, Issue 4, Pages 508–523 (Mi mz8572)

On the Order of Approximation by Riesz Means in Multiplicative Systems in the Classes $E_X[\varepsilon]$

T. V. Iofina

Saratov State University named after N. G. Chernyshevsky

Abstract: 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, Fejér kernel, Hardy space

DOI: https://doi.org/10.4213/mzm8572

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English version:
Mathematical Notes, 2011, 89:4, 484–498

Bibliographic databases:

UDC: 517.51
Revised: 08.09.2010

Citation: T. V. Iofina, “On the Order of Approximation by Riesz Means in Multiplicative Systems in the Classes $E_X[\varepsilon]$”, Mat. Zametki, 89:4 (2011), 508–523; Math. Notes, 89:4 (2011), 484–498

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz8572
• https://doi.org/10.4213/mzm8572
• http://mi.mathnet.ru/eng/mz/v89/i4/p508

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Chikina T.S., “Approximation by Zygmund-Riesz Means in the P-Variation Metric”, Anal. Math., 39:1 (2013), 29–44
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