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Topologies on spaces of vector-valued meromorphic functions

Part of: Entire and meromorphic functions, and related topics Topological linear spaces and related structures Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

Enrique Jordá
Enrique Jordá
Affiliation:
Departamento de Matemática AplicadaE. Politécnica Superior de AlcoyUniversidad Politécnica de ValenciaPlaza Ferrándiz y Carbonell 2 E-03801 Alcoy (Alicante)Spain e-mail: ejorda@mat.upv.es
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Abstract

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This paper presents two natural extensions of the topology of the space of scalar meromorphic functions M(Ω) described by Grosse-Erdmann in 1995 to spaces of vector-valued meromorphic functions M(ΩE). When E is locally complete and does not contain copies of ω we compare these topologies with the topology induced by the representation M (Ω, E) ≃ M(Ω)ε E recently obtained by Bonet, Maestre and the author.

MSC classification

Secondary: 46E40: Spaces of vector- and operator-valued functions 46A03: General theory of locally convex spaces 46E05: Lattices of continuous, differentiable or analytic functions 30D30: Meromorphic functions, general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 273 - 290
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Bochnack, J. and Siciak, J., ‘Analytic functions in topological vector spaces’, Studia Math. 39 (1971), 77–112.CrossRefGoogle Scholar
[2]Bonet, J., Jordá, E. and Maestre, M., ‘Vector-valued meromorphic functions’, Arch. Math. 79 (2002), 353–359.CrossRefGoogle Scholar
[3]Grosse-Erdmann, K.-G., The Borel Okada theorem revisted (Habilitation, Fernuniv. Hagen, 1993).Google Scholar
[4]Grosse-Erdmann, K.-G., ‘The locally convex topology on the space of meromorphic functions’, J. Austral. Math. Soc. (Series A) 59 (1995), 287–303.CrossRefGoogle Scholar
[5]Grosse-Erdmann, K.-G., ‘A weak criterion for vector-valued holomorphy’, Math. Proc. Cambridge Phil. Soc. 136 (2004), 399–411.CrossRefGoogle Scholar
[6]Grothendieck, A., ‘Sur certains espaces de fonctions holomorphes’, J. Reine Angew. Math. 192 (1953), 35–64.CrossRefGoogle Scholar
[7]Holdgrün, H. S., ‘Fastautomorphe Funktionen auf komplexen Räumen’, Math. Ann. 203 (1973), 35–64.CrossRefGoogle Scholar
[8]Jarchow, H., Locally convex spaces (B. G. Teubner, Stuttgart, 1981).CrossRefGoogle Scholar
[9]Jordá, E., Espacios de funciones meromorfas (Ph.D. Thesis, Universidad Politécnica de Valencia, Spain, 2001).Google Scholar
[10]Jordá, E., ‘Extension of vector-valued holomorphic and meromorphic functions’, Bull. Belgian Math. Soc. 12 (2005), 1–17.Google Scholar
[11]Kriegl, A. and Michor, P. W., The convenient setting of global analysis (American Mathematical Society, Providence, RI, 1997).CrossRefGoogle Scholar
[12]Meise, R. and Vogt, D., Introduction to functional analysis (Clarendon, Oxford, 1997).CrossRefGoogle Scholar
[13]Pérez Carreras, P. and Bonet, J., Barrelled locally convex spaces (North-Holland, Amsterdam, 1987).Google Scholar
[14]Rudin, W., Real and complex analysis 3rd edition (McGraw-Hill, New York, 1991).Google Scholar