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Vector-valued meromorphic functions

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Abstract.

A locally complete locally convex space E satisfies that every weakly meromorphic function defined on an open subset of \( \mathbb{C} \) with values in E is meromorphic if and only if E does not contain a countable product of copies of \( \mathbb{C} \). A characterization of locally complete spaces in the spirit of known characterizations of the (metric) convex compactness property is also given.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain¶ e-mail: jbonet@mat.upv.es, , , , , , ES

    J. Bonet

  2. Departamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Plaza Ferrándiz y Carbonell 2, E-03801 Alcoy (Alicante), Spain¶ e-mail: ejorda@mat.upv.es, , , , , , ES

    E. Jordá

  3. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, E-46100 Burjasot (Valencia), Spain¶ e-mail: manuel.maestre@uv.es, , , , , , ES

    M. Maestre

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  1. J. Bonet
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  2. E. Jordá
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  3. M. Maestre
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Eingegangen am 26. 1. 2001

RID="*)"

ID="*)"Eine überarbeitete Fassung ging am 31. 5. 2001 ein.

RID="1)"

ID="1)"The research of Bonet was supported in part by DGESIC Project no. PB97-0333 and the research Maestre by DGESIC Project no. PB96-0758.

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Bonet, J., Jordá, E. & Maestre, M. Vector-valued meromorphic functions. Arch. Math. 79, 353–359 (2002). https://doi.org/10.1007/PL00012457

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  • DOI: https://doi.org/10.1007/PL00012457

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