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Sbornik: Mathematics, 2011, Volume 202, Issue 2, Pages 279–306
DOI: https://doi.org/10.1070/SM2011v202n02ABEH004146 (Mi sm7630) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Best approximation of functions in $L_p$ by polynomials on affine system

P. A. Terekhin

Saratov State University named after N. G. Chernyshevsky
English version PDF (396 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2011v202n02ABEH004146
Abstract: Estimates of the best $L_p$-approximation of functions by polynomials in an affine system (system of dilations and translations), which are similar to well-known estimates due to Ul'yanov and Golubov for approximations in the Haar system, are obtained. An analogue of A. F. Timan and M. F. Timan's inequality is shown to hold under certain conditions on the generating function of the affine system; this analogue fails for the Haar system for $1<p<\infty$.
Bibliography: 10 titles.
Keywords: Haar system, system of dilations and translations, affine system, best approximation.
Received: 10.09.2009 and 19.06.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 2, Pages 131–158
DOI: https://doi.org/10.4213/sm7630
Bibliographic databases:
Document Type: Article
UDC: 517.518+517.982
MSC: 42C10, 41A10, 42C40
Language: English
Original paper language: Russian
Citation: P. A. Terekhin, “Best approximation of functions in $L_p$ by polynomials on affine system”, Mat. Sb., 202:2 (2011), 131–158; Sb. Math., 202:2 (2011), 279–306
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:61
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