Aicheng Geng, Fucai You, Chunyuan Zhao, Shuhui Shi, Xinfeng Huang, “Some Estimates for the Error in Fourier–Legendre Expansions of Functions of One Variable”, Mat. Zametki, 2016, Volume 99, Issue 5,Pages <nobr>652

Papers published in the English version of the journal

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

Aicheng Geng^a, Fucai You^a, Chunyuan Zhao^a, Shuhui Shi^a, Xinfeng Huang^b

^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.

Received: 15.08.2013
Revised: 04.03.2016

Language: English