A generalization of Abel and Dirichlet criteria (Q2208520)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A generalization of Abel and Dirichlet criteria |
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A generalization of Abel and Dirichlet criteria (English)
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3 November 2020
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This paper is aimed to extend the classical Abel and Dirichlet criteria of convergence to the case of series or functions with values in a Banach space (not necessarily carrying an ordering structure). The main idea was the replacement of the class of monotonic functions by that of functions with bounded variation. Several examples illustrating the theory are also included.
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Abel criterion
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Dirichlet criterion
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improper integral
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semi-convergent series
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