Abstract
In this paper, we analyze the linear structure of the family H e (G) of holomorphic functions on a domain G of the complex plane that are not analytically continuable beyond the boundary of G. We prove that H e (G) contains, except for zero, a dense algebra; and, under appropriate conditions, the subfamily of H e (G) consisting of boundary-regular functions contains dense vector spaces with maximal dimension as well as infinite dimensional closed vector spaces and large algebras. We also consider the case in which G is a domain of existence in a complex Banach space. The results obtained complete or extend a number of previous results by several authors.
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To Professor José Bonet Solves on His 60th Birthday
The author was partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P.
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Bernal-González, L. Vector spaces of non-extendable holomorphic functions. JAMA 134, 769–786 (2018). https://doi.org/10.1007/s11854-018-0025-z
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DOI: https://doi.org/10.1007/s11854-018-0025-z