Artículo
Universal Taylor series with maximal cluster sets
Autor/es | Bernal González, Luis
Bonilla Ramírez, Antonio Lorenzo Calderón Moreno, María del Carmen Prado Bassas, José Antonio |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2009-06 |
Fecha de depósito | 2016-01-29 |
Publicado en |
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Resumen | We link the overconvergence properties of certain Taylor series in
the unit disk to the maximality of their cluster sets, so connecting
outer wild behavior to inner wild behavior. Specifically, it is proved
the existence ... We link the overconvergence properties of certain Taylor series in the unit disk to the maximality of their cluster sets, so connecting outer wild behavior to inner wild behavior. Specifically, it is proved the existence of a dense linear manifold of holomorphic functions in the disk that are, except for zero, universal Taylor series in the sense of Nestoridis and, simultaneously, have maximal cluster sets along many curves tending to the boundary. Moreover, it is constructed a dense linear manifold of universal Taylor series having, for each boundary point, limit zero along some path which is tangent to the corresponding radius. Finally, it is proved the existence of a closed infinite dimensional manifold of holomorphic functions enjoying the two-fold wild behavior specified at the beginning. |
Cita | Bernal González, L., Bonilla Ramírez, A.L., Calderón Moreno, M.d.C. y Prado Bassas, J.A. (2009). Universal Taylor series with maximal cluster sets. |
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