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A note on the finitization of Abelian and Tauberian theorems

Powell, Thomas (2024)
A note on the finitization of Abelian and Tauberian theorems.
In: Mathematical Logic Quarterly, 2020, 66 (3)
doi: 10.26083/tuprints-00016186
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: A note on the finitization of Abelian and Tauberian theorems
Language: English
Date: 26 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2020
Place of primary publication: Weinheim
Publisher: Wiley-VCH
Journal or Publication Title: Mathematical Logic Quarterly
Volume of the journal: 66
Issue Number: 3
DOI: 10.26083/tuprints-00016186
Corresponding Links:
Origin: Secondary publication DeepGreen

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular Gödel's functional interpretation, which we use to establish quantitative versions of both of these results.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-161868
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Logic
Date Deposited: 26 Jan 2024 13:58
Last Modified: 21 Feb 2024 14:24
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/16186
PPN: 515715301
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