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...

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Detalhes bibliográficos
Autores: Carando, Daniel Germán, Defant, Andreas, Sevilla Peris, Pablo
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
Descrição
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.