Equiconvergence of two Fourier series
type: Item
instance of: scholarly article
title: Equiconvergence of two Fourier series
zbMATH Open document ID: 0828.42019
author: Mariana Marčoková
published in: Journal of Approximation Theory
publication date: 1995-07-05T00:00:00Z
review text: The authoress considers the generalized Jacobi polynomials \(\{Q_n(x): n= 0, 1,\dots; x\in [- 1, 1]\}\), which are orthonormal with respect to the weight function \[ w(x):= (1- x)^\alpha(1+ x)^\beta \exp[u(x)],\quad \alpha, \beta> -1, \] where \(u(x)\) is a real function satisfying some general conditions. She studies the Fourier expansion with respect to \(\{Q_n(x)\}\) of a function \(f\) such that the integral \(\int^{\pi/2}_{-\pi/2} f(\sin t) dt\) exists, and proves a comparison theorem on the equiconvergence of this expansion with an associated trigonometric Fourier series (in the case where \(\alpha, \beta> -1/2\)).
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 756622
zbMATH Keywords: generalized Jacobi polynomials
zbMATH Keywords: Fourier expansion
zbMATH Keywords: equiconvergence
zbMATH Keywords: trigonometric Fourier series
reviewed by: Ferenc Móricz
MaRDI profile type: Publication
full work available at URL: jath.1995.1012
OpenAlex ID: W1988408237
DOI: 10.1006/JATH.1995.1012
description: scientific article; zbMATH DE number 756622