Order estimates for best approximations and moduli of continuity of the sum of a trigonometric series with quasi-monotone coefficients
type: Item
instance of: scholarly article
title: Order estimates for best approximations and moduli of continuity of the sum of a trigonometric series with quasi-monotone coefficients
zbMATH Open document ID: 0794.42001
DOI: 10.1007/BF01250558
published in: Mathematical Notes
publication date: 1994-03-09T00:00:00Z
review text: For two classes of \(2 \pi\)-periodic functions with nonnegative Fourier coefficients \(a_ n\) such that \(a_ n n^{-\theta} \geq a_{n+1} (n+1)^{-\theta}\) \((\theta \geq 0)\) and \(\sum a_ n<\infty\) and, respectively, \(n a_ n \to 0\) as \(n \to \infty\), the author obtains order of best approximations and of the moduli of continuity.
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 42A32
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 484293
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: order
zbMATH Keywords: best approximations
zbMATH Keywords: moduli of continuity
author: A. S. Belov
MaRDI profile type: Publication
cites work: Q5337337
cites work: Q3937799
cites work: Subsequences of the partial sums of a trigonometric series which are everywhere convergent to zero
cites work: Fourier-Koeffizienten und Funktionenklassen
cites work: Q3292685
cites work: Über den Stetigkeitsmodul von Fourier-Reihen mit monotonen Koeffizienten
full work available at URL: https://doi.org/10.1007/bf01250558
OpenAlex ID: W1996915655
description: scientific article; zbMATH DE number 484293