On the trigonometric approximation of functions in a weighted Lipschitz class
type: Item
instance of: scholarly article
title: On the trigonometric approximation of functions in a weighted Lipschitz class
zbMATH Open document ID: 1465.42003
author: Uaday Singh
published in: The Journal of Analysis
publication date: 2021-05-21T00:00:00Z
review text: The author considered functions from weighted Lipschitz classes \(W\left( L^{r},w\right) \) and their conjugate ones. He proved two theorems on approximations of such functions by the \(C^{1}T\) means of its Fourier series with respect to the weighted norm. The function \( w\) was used as a measure of such approximations. The author used interesting assumptions on the function \(w,\) thanks to which it was possible to obtain the best orders of approximation. Some corollaries with generalization and improvement of various results available in the literature, for special functions \(w\) and selected matrix methods, were derived.
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 40G05
Mathematics Subject Classification ID: 41A81
zbMATH DE Number: 7350503
zbMATH Keywords: degree of approximation
zbMATH Keywords: weighted norm
zbMATH Keywords: Fourier series
zbMATH Keywords: conjugate function
reviewed by: W. Łenski
MaRDI profile type: Publication
full work available at URL: s41478-020-00267-5
OpenAlex ID: W3087695343
cites work: Q3704358
cites work: Approximation of functions belonging to the generalized Lipschitz class by \(C^1 \cdot N_p\) summability method of Fourier series
cites work: Pointwise approximation of \(2 \pi/r\)-periodic functions by matrix operators of their Fourier series with \(r\)-differences of the entries
cites work: Q274985
cites work: On the degree of approximation of functions in a weighted Lipschitz class by almost matrix summability method
cites work: On the degree of approximation of functions belonging to a Lipschitz class by Hausdorff means of its Fourier series
cites work: Trigonometric approximation of signals (functions) belonging to \(W(L^r,\xi(t))\) class by matrix \((C^1 \cdot N_p)\) operator
cites work: Trigonometric approximation of functions belonging to certain Lipschitz classes by C1⋅ T operator
cites work: Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series with the use of some parameters
cites work: On the trigonometric approximation of the generalized weighted Lipschitz class
cites work: Q4797357
DOI: 10.1007/S41478-020-00267-5
description: scientific article; zbMATH DE number 7350503