Mixed Bohr radius in several variables
Let K(Bℓnp , Bℓnq ) be the n-dimensional (p, q)-Bohr radius for holomorphic functions on Cn. That is, K(Bℓnp , Bℓnq ) denotes the greatest number r ≥ 0 such that for every entire function f(z) = Σ α aαzα in n-complex variables, we have the following (mixed) Bohr-type inequality: sup Σ |aαzα| ≤ sup |...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/117679 |
| Acesso em linha: | http://hdl.handle.net/11336/117679 |
| Access Level: | acceso abierto |
| Palavra-chave: | BOHR RADIUS DOMAINS OF CONVERGENCE FOR MONOMIAL EXPANSIONS HOMOGENEOUS POLYNOMIALS POWER SERIES UNCONDITIONAL BASES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let K(Bℓnp , Bℓnq ) be the n-dimensional (p, q)-Bohr radius for holomorphic functions on Cn. That is, K(Bℓnp , Bℓnq ) denotes the greatest number r ≥ 0 such that for every entire function f(z) = Σ α aαzα in n-complex variables, we have the following (mixed) Bohr-type inequality: sup Σ |aαzα| ≤ sup |f(z)|, z∈r·Bℓn z∈Bℓn α q p where Bℓn denotes the closed unit ball of the n-dimensional sequence space ℓn r . r For every 1 ≤ p, q ≤ ∞, we exhibit the exact asymptotic growth of the (p, q)-Bohr radius as n (the number of variables) goes to infinity. |
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