Tauberian theorems for sequences and the Katznelson--Tzafriri theorem
Abstract
In this note, we present an alternative proof of a quantified Tauberian theorem for vector-valued sequences first proved in Sei15Tauberian. 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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