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arXiv · 2502.15486

Tauberian theorems for sequences and the Katznelson--Tzafriri theorem

Andrew K. J. Pritchard·David Seifert
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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.

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Andrew K. J. Pritchard, David Seifert. 2025-02-21. Tauberian theorems for sequences and the Katznelson--Tzafriri theorem. https://arxiv.org/abs/2502.15486

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