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On the topological description of weighted inductive limits of spaces of holomorphic and harmonic functions

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Abstract.

A necessary condition is given for the case, that the topology in a weighted inductive limit of spaces of holomorphic functions can be described by the canonical weighted sup-norms. This leads to an easy scheme to construct counterexamples to the problem of projective description. Similar conditions are shown, under suitable assumptions, to be necessary and sufficient in the case of harmonic functions.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain, , , , , , ES

    José Bonet

  2. Fachbereich Mathematik, Bergische Universität, Gaußstraße 20, D-42097 Wuppertal, Germany, , , , , , DE

    Dietmar Vogt

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  1. José Bonet
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  2. Dietmar Vogt
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Received: 17.3.1998; revised version received 18.9.1988.

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Bonet, J., Vogt, D. On the topological description of weighted inductive limits of spaces of holomorphic and harmonic functions. Arch. Math. 72, 360–366 (1999). https://doi.org/10.1007/s000130050344

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  • DOI: https://doi.org/10.1007/s000130050344

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