Almost sure-sign convergence of Hardy-type Dirichlet series
Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series ∑ nann− s is uniformly a.s.- sign convergent (i.e., ∑ nεnann− s converges uniformly for almost all sequences of signs εn = ±1) but does not convergent absolutely, equals 1/2. We study...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/88537 |
| Acesso em linha: | http://hdl.handle.net/11336/88537 |
| Access Level: | acceso abierto |
| Palavra-chave: | Hardy spaces Dirichlet series Random series https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series ∑ nann− s is uniformly a.s.- sign convergent (i.e., ∑ nεnann− s converges uniformly for almost all sequences of signs εn = ±1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space. |
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