2000 character limit reached
Tauberian theorems for sequences and the Katznelson--Tzafriri theorem (2502.15486v2)
Published 21 Feb 2025 in math.FA
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.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.