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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-7,
author = {David Seifert},
title = {A quantified Tauberian theorem for sequences},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {183-192},
zbl = {1339.40008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-7}
}
David Seifert. A quantified Tauberian theorem for sequences. Studia Mathematica, Tome 231 (2015) pp. 183-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-7/