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Infinite dimensional holomorphic non-extendability and algebraic genericity

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Bernal González, Luis and Calderón Moreno, M. C. and Seoane-Sepúlveda, Juan B. (2017) Infinite dimensional holomorphic non-extendability and algebraic genericity. Linear Algebra and its Applications, 513 . pp. 149-159. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379516304815


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Abstract

In this note, the linear structure of the family H-e(G) of holomorphic functions in a domain G of a complex Banach space that are not holomorphically continuable beyond the boundary of G is analyzed. More particularly, we prove that H-e(G) contains, except for zero, a closed (and a dense) vector space having maximal dimension, as well as a maximally generated free algebra. The results obtained complete a number of previous ones by several author.


Item Type:Article
Uncontrolled Keywords:Lineability; Maximal spaceability; Maximal algebrability; Non-continuable holomorphic functions; Domain of existence; Balanced domain
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:40713
Deposited On:02 Feb 2017 10:03
Last Modified:02 Feb 2017 11:22

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