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 |
| Abstract: | 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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