A quantified Tauberian theorem for sequences
Functional Analysis
2019-02-14 v1
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 in [21].
Cite
@article{arxiv.1504.00560,
title = {A quantified Tauberian theorem for sequences},
author = {David Seifert},
journal= {arXiv preprint arXiv:1504.00560},
year = {2019}
}