On the strong summability of orthogonal series

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

It is well known that not every summability method implies the strong summability with any positive exponent. We give easygoing additional conditions on the terms of a positive regular Toeplitz-matrix implying the strong summability for any positive exponent. The classical (C, α > 0)- and Abel- summabilities satisfy our conditions plainly. We treat the generalized Abel, the Euler, the Riesz and the generalized de la Vallée Poussin methods, as well.

Original languageEnglish
Pages (from-to)163-174
Number of pages12
JournalActa Mathematica Hungarica
Volume81
Issue number1-2
Publication statusPublished - Oct 1998

Fingerprint

Orthogonal Series
Summability
Exponent
Toeplitz matrix
Euler
Imply
Term

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the strong summability of orthogonal series. / Leindler, L.

In: Acta Mathematica Hungarica, Vol. 81, No. 1-2, 10.1998, p. 163-174.

Research output: Contribution to journalArticle

@article{44b7a4230d5a480395757581660cc500,
title = "On the strong summability of orthogonal series",
abstract = "It is well known that not every summability method implies the strong summability with any positive exponent. We give easygoing additional conditions on the terms of a positive regular Toeplitz-matrix implying the strong summability for any positive exponent. The classical (C, α > 0)- and Abel- summabilities satisfy our conditions plainly. We treat the generalized Abel, the Euler, the Riesz and the generalized de la Vall{\'e}e Poussin methods, as well.",
author = "L. Leindler",
year = "1998",
month = "10",
language = "English",
volume = "81",
pages = "163--174",
journal = "Acta Mathematica Hungarica",
issn = "0236-5294",
publisher = "Springer Netherlands",
number = "1-2",

}

TY - JOUR

T1 - On the strong summability of orthogonal series

AU - Leindler, L.

PY - 1998/10

Y1 - 1998/10

N2 - It is well known that not every summability method implies the strong summability with any positive exponent. We give easygoing additional conditions on the terms of a positive regular Toeplitz-matrix implying the strong summability for any positive exponent. The classical (C, α > 0)- and Abel- summabilities satisfy our conditions plainly. We treat the generalized Abel, the Euler, the Riesz and the generalized de la Vallée Poussin methods, as well.

AB - It is well known that not every summability method implies the strong summability with any positive exponent. We give easygoing additional conditions on the terms of a positive regular Toeplitz-matrix implying the strong summability for any positive exponent. The classical (C, α > 0)- and Abel- summabilities satisfy our conditions plainly. We treat the generalized Abel, the Euler, the Riesz and the generalized de la Vallée Poussin methods, as well.

UR - http://www.scopus.com/inward/record.url?scp=0032221386&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032221386&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032221386

VL - 81

SP - 163

EP - 174

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 1-2

ER -