Article PDF
Avoid common mistakes on your manuscript.
References
Boland, P.,Holomorphic functions on nuclear spaces, Universidad de Santiago de Compostela, Spain, 1977.
Bremermann, H., Über die Äquivalenz dei pseudokonvexen Gebiete und der Holomorphiegebiete im Raum vonn Komplexen Veränderlichen,Math. Ann. 128 (1954), 63–91.
Colombeau, J. F., Infinite dimensionalC ∞ mappings with a given sequence of derivatives at a given point,J. Math. Anal. Appl., to appear.
Dineen, S., Surjective limits of locally convex spaces and their applications to infinite dimensional holomorphy,Bull. Soc. Math. France 103 (1975), 441–509.
Dineen, S., Noverraz, P. andSchottenloher, M., Le problème de Levi dans certains espaces vectoriels topologiques localement convexes,Bull. Soc. Math. France 104 (1976), 87–97.
Dubinsky, E.,A nuclear Fréchet space without the bounded approximation property, Institute of Mathematics, Polish Academy of Sciences, preprint, 1978.
Grauert, H. andFritzsche, K.,Several complex variables, Springer, New York-Heidelberg-Berlin, 1976.
Grothendieck, A., Sur les espaces (F) et (DF),Summa Brasil Math. 3 (1954), 57–123.
Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires,Memoirs Amer. Math. Soc. 16, Providence, Rhode Island, 1955.
Gruman, L., The Levi problem in certain infinite dimensional vector spaces,Illinois J. Math. 18 (1974), 20–26.
Gruman, L. andKiselman, C. O., Le problème de Levi dans les espaces de Banach à base,C. R. Acad. Sc. Paris 274 (1972), Série A, 1296–1298.
Hogbe-Nlend, H., Topologies et bornologies nucléaires associées. Applications,Ann. Inst. Fourier Grenoble 23 (1973), 89–104.
Hörmander, L.,An introduction to complex analysis in several variables, North-Holland and American Elsevier, Amsterdam-London-New York, 1973.
Josefson, B., A counterexample in the Levi problem, In:Proceedings on infinite dimensional holomorphy, Lecture Notes in Math.364, 168–177. Springer, Berlin-Heidelberg-New York, 1974.
Levi, E. E., Sulle ipersuperfici dello spazio a 4 dimensioni che possono essere frontiera del campo di esistenza di una funzioni analitica di due variabili complesse,Ann. Mat. Pura Appl. (3)18 (1911), 69–79.
Mitiagin, B. S. andZobin, N., Contre exemple à l’existence d’une base dans un espace de Fréchet nucléarie,C. R. Acad. Sc. Paris 279 (1974), Série A, 255–256, 325–327.
Nachbin, L., Uniformité d’holomorphie et type exponential, In:Séminaire Pierre Lelong 1970, Lecture Notes in Math.205, 216–224, Springer, Berlin-Heidelberg-New York, 1971.
Norguet, F., Sur les domaines d’holomorphie des fonctions uniformes de plusieurs variables complexes,Bull. Soc. Math. France 82 (1954), 137–159.
Noverraz, P.,Pseudo-convexité, convexité polynomiale et domaines d’holomorphie en dimension infinie, North-Holland and American Elsevier, Amsterdam-London-New York, 1973.
Noverraz, P., Approximation of holomorphic or plurisubharmonic functions in certain Banach spaces, In:Proceedings on infinite dimensional holomorphy, Lecture Notes in Math.364, 178–185, Springer, Berlin-Heidelberg-New York, 1974.
Noverraz, P., Pseudo-convexité et base de Schauder dans les elc, In:Séminaire Pierre Lelong 1973–1974, Lecture Notes in Math.474, 63–82, Springer, Berlin-Heidelberg-New York, 1975.
Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. VI. Domaines pseudoconvexes,Tokohu Math. J. 49 (1942), 15–22.
Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. IX. Domaines finis sans point critique intérieur,Japan J. Math. 23 (1953), 97–155.
Pomes, R., Solution du problème de Levi dans les espaces de Silva à base,C. R. Acad. Sc. Paris,278 (1974), Série A 707–710.
Schaefer, H. H.,Topological vector spaces, Springer, New York-Heidelberg-Berlin, 1971.
Schottenloher, M., The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition,Ann. Inst. Fourier Grenoble 26 (1976), 207–237.
Schwartz, L.,Radon measures on arbitrary topological spaces and cylindrical measures, Tata Institute of Fundamental Research, Bombay, and Oxford University Press, London 1973.
Author information
Authors and Affiliations
Additional information
This work was done when the first author was a guest at the Universidade Estadual de Campinas during the European Summer of 1978. His visit was financed by Fundação, de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Financiadora de Estudos e Projetos (FINEP).
Rights and permissions
About this article
Cite this article
Colombeau, JF., Mujica, J. The Levi problem in nuclear Silva spaces. Ark. Mat. 18, 117–123 (1980). https://doi.org/10.1007/BF02384685
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02384685