A quantified Tauberian theorem for sequences
Volume 227 / 2015
Studia Mathematica 227 (2015), 183-192
MSC: Primary 40E05, 47A05; Secondary 37A25.
DOI: 10.4064/sm227-2-7
Abstract
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 the author (2014).
