Hankel transforms of general monotone functions
We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real- valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not...
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:288468 |
| Acceso en línea: | https://ddd.uab.cat/record/288468 https://dx.doi.org/urn:doi:10.1007/978-3-030-12277-5_5 |
| Access Level: | acceso abierto |
| Palabra clave: | Hankel transform Boundedness Uniform convergence General monotonicity Cosine series |
| Sumario: | We show that the Hankel transform of a general monotone function converges uniformly if and only if the limit function is bounded. To this end, we rely on an Abel-Olivier test for real- valued functions. Analogous results for cosine series are derived as well. We also show that our statements do not hold without the general monotonicity assumption in the case of cosine integrals and series. |
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