Analogues of some Tauberian theorems for bounded variation

R. Patterson

doi:10.1007/s10474-008-8015-8

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Acta Mathematica Hungarica

Volume/Issue:: Volume 122: Issue 3

Analogues of some Tauberian theorems for bounded variation

Author:

R. Patterson

R. Patterson University of North Florida Department of Mathematics and Statistics Jacksonville Florida 32224 USA

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Pages:: 255–271

Online Publication Date:: 13 Jul 2008

Publication Date:: 01 Feb 2009

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10474-008-8015-8

Keywords:: divergent double sequences; subsequences of a double sequences; Pringsheim limit point; P-convergent; P-divergent; RH-regular; primary 40B05; secondary 40C05

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Abstract

In this paper definitions for “bounded variation”, “subsequences”, “Pringsheim limit points”, and “stretchings” of a double sequence are presented. Using these definitions and the notion of regularity for four dimensional matrices, the following two questions will be answered. First, if there exists a four dimensional regular matrix A such that Ay = Σ_k,l=1,1^∞∞a_m,n,k,ly_k,l is of bounded variation (BV) for every subsequence y of x, does it necessarily follow that x ∈ BV? Second, if there exists a four dimensional regular matrix A such that Ay ∈ BV for all stretchings y of x, does it necessarily follow that x ∈ BV? Also some natural implications and variations of the two Tauberian questions above will be presented.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
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	0236-5294 (Print)
ISSN	1588-2632 (Online)