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...
| Autores: | , , , |
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| 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 |
| 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. |
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