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Vector spaces of non-extendable holomorphic functions

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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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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, 41080, Sevilla, Spain

    Luis Bernal-González

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  1. Luis Bernal-González
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Correspondence to Luis Bernal-González.

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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

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