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Vector spaces of non-extendable holomorphic functions


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Opened Access Vector spaces of non-extendable holomorphic functions

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Author: Bernal González, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2018-02
Published in: Journal d'Analyse Mathématique, 134 (2), 769-786.
Document type: Article
Abstract: 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.
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DOI: 10.1007/s11854-018-0025-z

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