Powell, Thomas (2020)
A note on the finitization of Abelian and Tauberian theorems.
In: Mathematical Logic Quarterly, 66 (3)
doi: 10.1002/malq.201900076
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2020 |
| Autor(en): | Powell, Thomas |
| Art des Eintrags: | Bibliographie |
| Titel: | A note on the finitization of Abelian and Tauberian theorems |
| Sprache: | Englisch |
| Publikationsjahr: | 2020 |
| Ort: | Weinheim |
| Verlag: | Wiley-VCH |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematical Logic Quarterly |
| Jahrgang/Volume einer Zeitschrift: | 66 |
| (Heft-)Nummer: | 3 |
| DOI: | 10.1002/malq.201900076 |
| Zugehörige Links: | |
| Kurzbeschreibung (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. |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Logik |
| Hinterlegungsdatum: | 31 Jan 2024 10:13 |
| Letzte Änderung: | 31 Jan 2024 10:13 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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A note on the finitization of Abelian and Tauberian theorems. (deposited 26 Jan 2024 13:58)
- A note on the finitization of Abelian and Tauberian theorems. (deposited 31 Jan 2024 10:13) [Gegenwärtig angezeigt]
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