A note on the absolute summability of Fourier series by Bosanquet-Linfoot method
type: Item
instance of: scholarly article
title: A note on the absolute summability of Fourier series by Bosanquet-Linfoot method
zbMATH Open document ID: 1023.42003
published in: Real Analysis Exchange
publication date: 2003-01-05T00:00:00Z
review text: The main result reads as follows. Let \(\Phi(t)=(f(x+t)+f(x-t))/2\) and \(\alpha\geq 0.\) If \(t^{-\alpha}\int_0^t(t-u)^{\alpha-1}\Phi(u) du\) is of bounded variation on \((0,\pi),\) then the Fourier series of an integrable \(2\pi\)-periodic function \(f\) is summable \(|\alpha,\beta|\) for all \(\beta\geq 1.\) In earlier results the range of \(\beta\) was narrower.
reviewed by: Elijah Liflyand
Mathematics Subject Classification ID: 42A24
Mathematics Subject Classification ID: 40G99
Mathematics Subject Classification ID: 40F05
zbMATH DE Number: 1848925
zbMATH Keywords: absolute summability of Fourier series
zbMATH Keywords: Bosanquet-Linfoot method
zbMATH Keywords: Nevanlinna method
author: Ganesh Datta Dikshit
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1848925