Tauberian conditions under which convergence follows from Abel summability (Q602829)
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scientific article; zbMATH DE number 5810842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tauberian conditions under which convergence follows from Abel summability |
scientific article; zbMATH DE number 5810842 |
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Tauberian conditions under which convergence follows from Abel summability (English)
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5 November 2010
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The authors prove that if \((u(n))\) is Abel summable to \(s\) and if \((u(n))\) is one-sided slowly oscillating, then \(u(n)\) converges to \(s\). The proof of the result is based on a corollary to Karamata's main theorem [\textit{J.\ Karamata}, Math.\ Z. 32, 319--320 (1930; JFM 56.0210.01)].
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Abel summability
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one-sided slow oscillation
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Tauberian conditions
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