Frechet spaces of general Dirichlet series

[EN] Inspired by a recent article on Frechet spaces of ordinary Dirichlet series Sigma a(n)n(-s) due to J. Bonet, we study topological and geometrical properties of certain scales of Frechet spaces of general Dirichlet spaces Sigma a(n)e(-lambda ns) focus on the Frechet space of lambda-Dirichlet ser...

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Detalles Bibliográficos
Autores: Defant, Andreas, Fernández Vidal, Tomás, Schoolmann, Ingo, Sevilla Peris, Pablo|||0000-0001-5222-4768
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/187680
Acceso en línea:https://riunet.upv.es/handle/10251/187680
Access Level:acceso abierto
Palabra clave:General Dirichlet series
Abscissas of convergence
Frechet spaces
Hardy spaces
Almost periodic functions
MATEMATICA APLICADA
Descripción
Sumario:[EN] Inspired by a recent article on Frechet spaces of ordinary Dirichlet series Sigma a(n)n(-s) due to J. Bonet, we study topological and geometrical properties of certain scales of Frechet spaces of general Dirichlet spaces Sigma a(n)e(-lambda ns) focus on the Frechet space of lambda-Dirichlet series Sigma a(n)e(-lambda ns) which have limit functions bounded on all half planes strictly smaller than the right half plane [Re > 0]. We develop an abstract setting of pre-Frechet spaces of lambda-Dirichlet series generated by certain admissible normed spaces of lambda-Dirichlet series and the abscissas of convergence they generate, which allows also to define Frechet spaces of lambda-Dirichlet series for which a(n)e(-lambda n/k) for each k equals the Fourier coefficients of a function on an appropriate lambda-Dirichlet group.