Tauberian theorems for Abel limitability method
İbrahim Çanak, Ümit Totur (2008)
Open Mathematics
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This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.
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Tauberian theorems for Abel limitability method
Tauberian conditions for a general limitable method.
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A quantified Tauberian theorem for sequences
David Seifert (2015)
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The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by...