Hostname: page-component-7dd5485656-kp629 Total loading time: 0 Render date: 2025-10-31T02:53:43.206Z Has data issue: false hasContentIssue false
  • English
  • Français

On the holomorphical classification of spaces of holomorphic germs

Published online by Cambridge University Press:  22 January 2016

Jorge Aragona
Jorge Aragona*
Affiliation:
Universidade de São Paulo, Instituto de Matemática e Estatistica São Paulo, Brasil
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K be a compact set in a complex metrizable locally convex space E and F a complex Banach space. The study of the space of holomorphic germs ℋ(K; F) endowed with the Nachbin topology was undertaken by several authors.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 84 , December 1981 , pp. 85 - 118
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[A-Mu] Aviles, P. and Mujica, J., Holomorphic germs and homogeneous polynomials on quasi—normale metrizable spaces, Rendiconti di Matematica, to appear. Google Scholar
[B] Barroso, J.A., Topologias nos espaços de aplicações holomorfas entre espaços localmente convexos, An. Acad. Bras, de Ciências, 43, no. 3/4 (1971), 527–546.Google Scholar
[BMN] Barroso, J. A., Matos, M. A. and Nachbin, L., On holomorphy versus linearity in classifying locally convex spaces, Infinite Dimensional Holomorphy and Applications (Editor: Matos, M.C.), North-Holland Mathematics Studies (1977).Google Scholar
[Bi-Me] Bierstedt, K.D. and Meise, R. , ℋ(K) et (ℋ(U); ) sur des espaces metrisables nucléaires ou de Schwartz, C. R. Acad. Sc. Paris, t. 283 (1976).Google Scholar
[Ch] Chae, S.B., Holomorphic germs on Banach spaces, Ann. Inst. Fourier, 21, 3 (1971), 107–141.Google Scholar
[D] Dineen, S., Holomorphic functions on strong duals of Fréchet-Montel spaces, Infinite Dimensional Holomorphy and Applications (Editor: Matos, M.C.), North-Holland Mathematics Studies (1977).Google Scholar
[G] Grothendieck, A., Espaces vectoriels topologiques, Publicação da Sociedade Matemática de São Paulo, 3° Edição (1964).Google Scholar
[H] Horvath, J., Topological vector spaces and distributions, Vol. I, Addison Wesley (1966).Google Scholar
[M] Matos, M.C., On locally convex spaces with the Montel property, Functional Analysis (Editor: de, D.G. Figueiredo), Marcel Dekker (1976), 245–250.Google Scholar
[Mu] Mujica, J., Spaces of germs of holomorphic functions, Advances in Mathematics, 4 (1979).Google Scholar
[N1] Nachbin, L., A glimpse at infinite dimensional holomorphy, Proceedings on Infinite Dimensional Holomorphy (Editors: Hayden, T.L.; Suffridge, T.J.), Lecture Notes in Mathematics, Springer-Verlag, 364 (1974), 69–78.Google Scholar
[N2] Nachbin, L., Some holomorphically significant properties of locally convex spaces, Functional Analysis (Editor: de, D.G. Figueiredo), Marcel Dekker (1976), 251–277.Google Scholar
[S] Soraggi, L.R., Partes limitadas nos espaços de germes de aplicações holomorfas, Thesis, Universidade Federal do Rio de Janeiro, no. 4 (1976).Google Scholar
[W] Wanderley, A. J. M., Germes de aplicações holomorfas em espaços localmente convexos, Thesis, Universidade Federal do Rio de Janeiro.Google Scholar