Artículo
Vector spaces of non-extendable holomorphic functions
Autor/es | Bernal González, Luis |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2018-02 |
Fecha de depósito | 2018-04-04 |
Publicado en |
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Resumen | In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that are not analytically continuable beyond the boundary of G is analyzed. We prove that He(G) contains, ... In this paper, the linear structure of the family He(G) of holomorphic functions in a domain G of the complex plane that are not analytically continuable beyond the boundary of G is analyzed. We prove that He(G) contains, except for zero, a dense algebra; and, under appropriate conditions, the subfamily of He(G) consisting of boundary-regular functions contains dense vector spaces with maximal dimension, as well as infinite dimensional closed vector spaces and large algebras. The case in which G is a domain of existence in a complex Banach space is also considered. The results obtained complete or extend a number of previous ones by several authors. |
Agencias financiadoras | Junta de Andalucía Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | FQM-127
P08-FQM-03543 MTM2012-34847-C02-01 MTM2015-65242-C2-1-P |
Cita | Bernal González, L. (2018). Vector spaces of non-extendable holomorphic functions. Journal d'Analyse Mathématique, 134 (2), 769-786. |
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