Necessary and sufficient Tauberian condition for both Cesàro and Abel summability (Q6554587)
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scientific article; zbMATH DE number 7864379
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Necessary and sufficient Tauberian condition for both Cesàro and Abel summability |
scientific article; zbMATH DE number 7864379 |
Statements
Necessary and sufficient Tauberian condition for both Cesàro and Abel summability (English)
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12 June 2024
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The Weakly-Vanishing Mean Oscillation (W-VMO) property is introduced and its relation with some Tauberian conditions in the literature is investigated. Then, it is shown that this property is a necessary and sufficient condition under which convergence follows from Abel and Cesàro summability. Moreover, it is examined whether Cesàro summability can be obtained from Abel summability under this condition and whether this condition is necessary for this case.
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Abel summability
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Cesàro summability
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power series
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Tauberian theory
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weakly-vanishing mean oscillation
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