Dense-lineability of sets of Birkhoff-universal functions with rapid decay
Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal,...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87511 |
| Acceso en línea: | https://hdl.handle.net/11441/87511 https://doi.org/10.1016/j.jmaa.2009.08.049 |
| Access Level: | acceso abierto |
| Palabra clave: | Birkhoff-universal function Dense lineability Arakelian set Infinite order differential operator Growth of entire functions |
| Sumario: | Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal, such that each function in M has overall growth faster than ψ and, in addition, exp(|z|α)f(z) → 0 (z → ∞, z ∈ A) for all α < 1/2 and f ∈ M. With slightly more restrictive conditions on A, we get that the last property also holds for the action T f of certain holomorphic operators T. Our results unify, extend and complete recent work by several authors. |
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