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Matematicheskie Zametki, 2016, Volume 99, Issue 5, paper published in the English version journal (Mi mzm11228)  
Papers published in the English version of the journal

Some Estimates for the Error in Fourier–Legendre Expansions of Functions of One Variable

Aicheng Genga, Fucai Youa, Chunyuan Zhaoa, Shuhui Shia, Xinfeng Huangb

a Shenyang Institute of Engineering, Shenyang, China
b Huafu Middle School, Shenzhen, China
Abstract: Some issues concerning expansions of functions in Fourier–Legendre series is considered in $L_2[-1,1]$. In particular, the rate of their convergence in the classes of functions characterized by the generalized modulus of continuity are estimated, and estimates of the remainder terms are obtained.
Keywords: Fourier–Legendre series, modulus of continuity, best approximation, estimates of remainder terms, Kolmogorov $n$-width.
Funding agency Grant number
National Natural Science Foundation of China 11401392
Scientific Research Fund of Liaoning Provincial Education Department L2015378
Liaoning Educational Committee Foundation L2014525
This work was supported by the Natural Science Foundation of China (grant No. 11401392), by the Scientific Research Fund of Liaoning Provincial Education Department (grant no. L2015378), and Liaoning Educational Committee Foundation under contract no. L2014525.
Received: 15.08.2013
Revised: 04.03.2016
English version:
Mathematical Notes, 2016, Volume 99, Issue 5, Pages 652–661
DOI: https://doi.org/10.1134/S0001434616050047
Bibliographic databases:
Document Type: Article
Language: English
Citation: Aicheng Geng, Fucai You, Chunyuan Zhao, Shuhui Shi, Xinfeng Huang, “Some Estimates for the Error in Fourier–Legendre Expansions of Functions of One Variable”, Math. Notes, 99:5 (2016), 652–661
Citation in format AMSBIB
\Bibitem{GenYouZha16}
\by Aicheng Geng, Fucai You, Chunyuan Zhao, Shuhui Shi, Xinfeng Huang
\paper Some Estimates for the Error in Fourier--Legendre Expansions of Functions of One Variable
\jour Math. Notes
\yr 2016
\vol 99
\issue 5
\pages 652--661
\mathnet{http://mi.mathnet.ru/mzm11228}
\crossref{https://doi.org/10.1134/S0001434616050047}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3519302}
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\elib{https://elibrary.ru/item.asp?id=26871038}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84977110681}
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