A quantified Tauberian theorem for sequences

@article{DavidSeifert2015,
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).},
author = {David Seifert},
journal = {Studia Mathematica},
keywords = {Ingham's theorem; Tauberian theorem; sequences; rates of decay; Katznelson-Tzafriri theorem},
language = {eng},
number = {2},
pages = {183-192},
title = {A quantified Tauberian theorem for sequences},
url = {http://eudml.org/doc/285800},
volume = {227},
year = {2015},
}

TY - JOUR
AU - David Seifert
TI - A quantified Tauberian theorem for sequences
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 2
SP - 183
EP - 192
AB - 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).
LA - eng
KW - Ingham's theorem; Tauberian theorem; sequences; rates of decay; Katznelson-Tzafriri theorem
UR - http://eudml.org/doc/285800
ER -