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Tauberian Constants for Double Series
Author(s) -
Mirza M. Y.,
Thorpe B.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798005754
Subject(s) - abelian and tauberian theorems , section (typography) , series (stratigraphy) , notation , mathematics , constant (computer programming) , matrix (chemical analysis) , pure mathematics , discrete mathematics , arithmetic , computer science , paleontology , materials science , composite material , biology , programming language , operating system
The object of this paper is to extend a result of Agnew in [ 1 ] for single series to double series, and so enable Tauberian constants between matrix transformations of double sequences to be calculated using the technique that many authors have used previously for single sequences (see, for instance, [ 2 , 3 , 8 ]). This method (see below) gives the best possible Tauberian constants in the form of certain upper limits, and we attempt to calculate these for Cesàro summability with various known Tauberian conditions. In Section 2, we introduce our notation and review earlier work. In Section 3, we prove our main result, and we discuss applications to Cesàro summability in Section 4.