Tauberian theorems for sequences and the Katznelson--Tzafriri theorem
Functional Analysis
2025-04-10 v2
Abstract
In this note, we present an alternative proof of a quantified Tauberian theorem for vector-valued sequences first proved in \cite{Sei15_Tauberian}. The theorem relates the decay rate of a bounded sequence with properties of a certain boundary function. We present a slightly strengthened version of this result, and illustrate how it can be used to obtain quantified versions of the Katznelson--Tzafriri theorem as well as results on Ritt operators.
Cite
@article{arxiv.2502.15486,
title = {Tauberian theorems for sequences and the Katznelson--Tzafriri theorem},
author = {Andrew K. J. Pritchard and David Seifert},
journal= {arXiv preprint arXiv:2502.15486},
year = {2025}
}
Comments
Accepted for publication in the IWOTA 2024 proceedings