On absolute matrix summability of the conjugate series
type: Item
instance of: scholarly article
zbMATH Open document ID: 1017.42003
publication date: 2003-08-28T00:00:00Z
Mathematics Subject Classification ID: 42A24
Mathematics Subject Classification ID: 42A50
zbMATH DE Number: 1704364
zbMATH Keywords: absolute summability
zbMATH Keywords: matrix summability
zbMATH Keywords: conjugate series
zbMATH Keywords: Fourier series
MaRDI profile type: Publication
author: U. K. Mishra
author: J. K. Sahu
title: On absolute matrix summability of the conjugate series
published in: Ranchi University Mathematical Journal
review text: The authors have made an effort to generalize an unpublished work of \textit{S. Rath} [Ph.D. Thesis, Berhamprur University, India, 133-153 (1977)] concerning \(|N,p_n|\)-summability of the conjugate series of the Fourier series at a point. They have replaced the Nörlund matrix by the infinite matrix \((a_{nk})\) \((n,k= 0,1\dots)\) satisfying some conditions. The statement of the theorem is incomplete in the sense that the only hypothesis \(\psi(t)\log{a\over t}\in \text{BV}(0,\pi)\), assumed for the generating function of the series, is not sufficient to ensure \(\int^\pi_0\log{a\over t}|d\psi(t)|< \infty\), which is being used in the proof of the theorem on page 50; line 3. The paper contains some misprints which cause inconvenience to the readers.
reviewed by: Prem Chandra
description: scientific article; zbMATH DE number 1704364