Approximation by Fourier sums of functions with slowly decreasing Fourier coefficients
type: Item
instance of: scholarly article
title: Approximation by Fourier sums of functions with slowly decreasing Fourier coefficients
zbMATH Open document ID: 0623.42002
DOI: 10.1007/BF01056650
author: A. I. Stepanets
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Suppose that \(f\in L[0,\pi)\) and that \(a_ k=a_ k(f)\), \(b_ k=b_ k(f)\) \(k=0,1,..\). are its Fourier coefficients. Suppose also that \(\psi\) (k) is a function of natural k and \(\beta\in R\). A functional class \(L^{\psi}_{\beta}\) is introduced by the expression \[ \sum^{\infty}_{k=1}\frac{1}{\psi (k)}(a_ k \cos (kx+\beta \pi /2)+b_ k \sin (kx+\beta \pi /2). \] Approximate properties of the classes of \(L^{\psi}_{\beta}\) type are studied. Some asymptotic estimates are also established.
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 42A32
zbMATH DE Number: 4011135
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: asymptotic estimates
MaRDI profile type: Publication
cites work: Q5791318
cites work: Q5621638
cites work: Q3937831
cites work: Approximation of periodic functions by Fourier sums in the mean
full work available at URL: https://doi.org/10.1007/bf01056650
OpenAlex ID: W2008055422
description: scientific article; zbMATH DE number 4011135