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Analysis Mathematica
Article
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Preprint . 2011
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Analysis Mathematica
Article . 2012 . Peer-reviewed
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Article . 2012
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https://dx.doi.org/10.48550/ar...
Article . 2011
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Uniform approximation of Poisson integrals of functions from the class H ω by de la Vallée Poussin sums

Uniform approximation of Poisson integrals of functions from the class \(H_\omega\) by de la Vallée Poussin sums
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 21 Nov 2012Embargo end date: 01 Jan 2011 English Publisher:Springer Science and Business Media LLCJournal:Analysis Mathematica, volume 38, pages 305-325 (issn: 0133-3852, eissn: 1588-273X, Copyright policy )
Authors: Serdyuk, A. S.; Ovsii, Ie. Yu.;

doi: 10.1007/s10476-012-0403-1 , 10.48550/arxiv.1104.3060

arXiv: 1104.3060

Uniform approximation of Poisson integrals of functions from the class H ω by de la Vallée Poussin sums

Abstract

We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vall��e Poussin sums on the sets C^{q}_��H_��of Poisson integrals of functions from the class H_��generated by convex upwards moduli of continuity ��(t) which satisfy the condition ��(t)/t\to\infty as t\to 0. As an implication, a solution of the Kolmogorov-Nikol'skii problem for de la Vall��e Poussin sums on the sets of Poisson integrals of functions belonging to Lipschitz classes H^��, 0

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Keywords

Kolmogorv-Nikol'skii problem, asymptotice equalities, Mathematics - Classical Analysis and ODEs, de la Vallée Poussin sums, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 42A10, Approximation by other special function classes

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Top 10%
Average
Green
bronze