On \(\Lambda\)-strong convergence of numerical sequences and Fourier series
type: Item
instance of: scholarly article
title: On \(\Lambda\)-strong convergence of numerical sequences and Fourier series
zbMATH Open document ID: 0708.42004
DOI: 10.1007/BF01952063
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: The author obtains several results concerning the \(\Lambda\)-strong convergence of numerical sequences and Fourier series. In section 2 the author shows that the class c(\(\Lambda\)) of \(\Lambda\)-strongly convergent sequences of complex numbers endowed with the norm \(\| \cdot \|_{c(\Lambda)}\) is a Banach space and that it has a Schauder basis. Let C be the Banach space of the \(2\pi\) periodic complex-valued continuous functions endowed with the norm \(\| f\|_ C=\max_{t}f(t)\). In section 3 of this paper the author establishes that the class S(\(\Lambda\)) of functions \(f\in C\) whose Fourier series converges uniformly \(\Lambda\)-strongly on [0,2\(\pi\)), endowed with a suitable norm is a Banach space. In section 4, results of section 3 are reformulated by substituting the \(L_ p\)-metric for C-metric.
Mathematics Subject Classification ID: 42A20
zbMATH DE Number: 4163475
zbMATH Keywords: \(\Lambda \) -strong convergence
zbMATH Keywords: Schauder basis
author: Ferenc Móricz
reviewed by: Y. Sitaraman
MaRDI profile type: Publication
cites work: Note on the Strong Summability of Series
cites work: On the Banach space of strongly convergent trigonometric series
cites work: On strong convergence of trigonometric and Fourier series
cites work: Q3254471
full work available at URL: https://doi.org/10.1007/bf01952063
OpenAlex ID: W2033323739
description: scientific article; zbMATH DE number 4163475