Skip to main content
SpringerLink
Log in

Domains of holomorphy in (DFC)-spaces

  • Conference paper
  • First Online:
Functional Analysis, Holomorphy, and Approximation Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 843))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bremermann, H., Über die Äquivalenz der pseudokonvexen Gebiete und der Holomorphiegebiete im Raum von n Komplexen Veränderlichen. Math. Ann. 128 (1954), 63–91.

    Article  MathSciNet  MATH  Google Scholar 

  2. Cartan, H.-Thullen, P., Regularitäts — und Konvergenzbereiche Math. Ann. 106 (1932), 617–647.

    Article  MathSciNet  MATH  Google Scholar 

  3. Colombeau, J.F., Infinite dimensional C∞ mappings with a given sequence of derivatives at a given point. J. Math. Anal. Appl. 71 (1979), 95–104.

    Article  MathSciNet  MATH  Google Scholar 

  4. Colombeau, J.F.-Mujica, J., The Levi problem in nuclear Silva spaces. Ark. Mat. (to appear)

    Google Scholar 

  5. Dineen, S., Surjective limits of locally convex spaces and their applications to infinite dimensional holomorphy. Bull. Soc. Math. France 103 (1975), 441–509.

    MathSciNet  MATH  Google Scholar 

  6. Dineen, S., Holomorphic functions on strong duals of Fréchet-Montel spaces. In: Infinite Dimensional Holomorphy and Applications, edited by M.C. Matos, pp. 147–166. North Holland, Amsterdam, 1977.

    Chapter  Google Scholar 

  7. Dineen, S.-Noverraz, Ph.-Schottenloher, M., Le problème de Levi dans certains espaces vectoriels topologiques localement convexes. Bull. Soc. Math. France 104 (1976), 87–97.

    MathSciNet  MATH  Google Scholar 

  8. Grauert, H.-Fritzsche, K., Several Complex Variables, Springer, New York, 1976.

    Book  MATH  Google Scholar 

  9. Gruman, L., The Levi problem in certain infinite dimensional vector spaces. Illinois J. Math. 18 (1974), 20–26.

    MathSciNet  MATH  Google Scholar 

  10. Gruman, L.-Kiselman, C.O., Le problème de Levi dans les espaces de Banach à base. C.R. Acad. Sc. Paris 274 (1972), Série A, 1296–1298.

    MathSciNet  MATH  Google Scholar 

  11. Hirschowitz, A., Prolongement analytique en dimension infinie. Ann. Inst. Fourier (Grenoble) 22 (1972), 255–292.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hollstein, R., (DCF)-Räume und lokalkonvexe Tensorprodukte. Arch. Math. (Basel) 29 (1977), 524–531.

    Article  MathSciNet  MATH  Google Scholar 

  13. Hollstein, R., Tensorprodukte von stetigen linearen Abbildungen in (F)-und (DCF)-Räumen. J. reine angew. Math. 301 (1978), 191–204.

    MathSciNet  MATH  Google Scholar 

  14. Hörmander, L., An Introduction to Complex Analysis in Several Variables. North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  15. Horváth, J., Topological Vector Spaces and Distributions, Vol.I. Addison-Wesley, Reading, Massachusetts, 1966.

    Google Scholar 

  16. Josefson, B., A counterexample in the Levi problem. In: Proceedings on Infinite Dimensional Holomorphy, edited by T.L. Hayden and T.J. Suffridge, pp. 168–177. Lecture Notes in Mathematics 364. Srpinger, Berlin, 1974.

    Chapter  Google Scholar 

  17. Kelley, J.L., General Topology. Van Nostrand, Princenton, New Jersey, 1955.

    MATH  Google Scholar 

  18. Köthe, G., Topological Vector Spaces I. Springer, Berlin, 1969.

    MATH  Google Scholar 

  19. 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. Math. Pura Appl. (3) 18 (1911), 69–79.

    Article  MATH  Google Scholar 

  20. Ligocka, E., A local factorization of analytic functions and its applications. Studia Math. 47 (1973), 239–252.

    MathSciNet  MATH  Google Scholar 

  21. Mujica, J., The Oka-Weil theorem in locally convex spaces with the approximation property. Séminaire Paul Krée 1977–1978, exposé no 3, Institut Henri Poincaré, Paris, 1979.

    MATH  Google Scholar 

  22. Nachbin, L. Topology on Spaces of Holomorphic Mappings, Springer, Berlin, 1969.

    Book  MATH  Google Scholar 

  23. Norguet, F., Sur les domaines d'holomorphie des fonctions uniformes de plusieurs variables complexes. Bull. Soc. Math. France 82 (1954), 137–159.

    MathSciNet  MATH  Google Scholar 

  24. Noverraz, Ph., Pseudo-Convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie. North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  25. Noverraz, Ph., Sur le théorème de Cartan-Thullen-Oka en dimension infinie. In: Séminaire Pierre Lelong Année 1971–1972, pp. 59–68. Lecture Notes in Mathematics 332. Springer, Berlin, 1973.

    Google Scholar 

  26. Noverraz, Ph., Approximation of holomorphic or plurisubharmonic functions in certain Banach spaces. In: Proceedings on Infinite Dimensional Holomorphy, edited by T.L. Hayden and T.J. Suffridge, pp. 178–185. Lecture Notes in Mathematics 364. Springer, Berlin, 1974.

    Chapter  Google Scholar 

  27. Noverraz, Ph., Pseudo-convexité et base de Schauder dans les elc. In: Séminaire Pierre Lelong Année 1973–1974, pp. 63–82. Lecture Notes in Mathematics 474. Springer, Berlin, 1975.

    Chapter  Google Scholar 

  28. Oka, K., Sur les fonctions analytiques de plusieurs variables complexes. IX. Domaines finis sans point critique intérieur. Japan J. Math. 23 (1953), 97–155.

    MathSciNet  MATH  Google Scholar 

  29. 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.

    MathSciNet  MATH  Google Scholar 

  30. Schottenloher, M., Das Leviproblem in unendlichdimensionalen Räumen mit Schauderzerlegung. Habilitationsschrift, Universität München, 1974.

    Google Scholar 

  31. 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.

    Article  MathSciNet  MATH  Google Scholar 

  32. Schottenloher, M., Polynomial approximation on compact sets. In: Infinite Dimensional Holomorphy and Applications, edited by M.C. Matos, pp. 379–391. North-Holland, Amsterdam, 1977.

    Chapter  Google Scholar 

  33. Schwartz, L., Produits tensoriels topologiques d'espaces vectoriels topologiques. Espaces vectoriels topologiques nucléaires. Applications. Séminaire Schwartz 1953–1954. Faculté des Sciences de Paris, 1954.

    Google Scholar 

  34. Schwartz, L., Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures. Tata Institute of Fundamental Research, Bombay, and Oxford University Press, London, 1973.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática, Universidade Estadual de Campinas, Caixa Postal 1170, 13100, Campinas, SP, Brasil

    Jorge Mujica

Authors
  1. Jorge Mujica
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Silvio Machado

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Mujica, J. (1981). Domains of holomorphy in (DFC)-spaces. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089287

Download citation

  • DOI: https://doi.org/10.1007/BFb0089287

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10560-2

  • Online ISBN: 978-3-540-38529-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation