One-sided Tauberian conditions and double sequences

U. Stadtmüller

doi:10.1023/a:1022362400453

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 45: Issue 1-2

One-sided Tauberian conditions and double sequences

Author:

U. Stadtmüller

U. Stadtmüller Universität Ulm Abt. f. Zahlen- u. Wahrscheinlichkeitstheor e D-89069 Ulm Germany

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Pages:: 135–146

Online Publication Date:: 03 Jan 2005

Publication Date:: 01 Sep 2002

Article Category:: Research Article

DOI:: https://doi.org/10.1023/a:1022362400453

Keywords:: double sequences; inverse theorem; power series methods; one-sided Tauberian condition

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Abstract

We give a theorem of Vijayaraghavan type for summability methods for double sequences, which allows a conclusion from boundedness in a mean and a one-sided Tauberian condition to the boundedness of the sequence itself. We apply the result to certain power series methods for double sequences improving a recent Tauberian result by S. Baron and the author [4].

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)