Skip to main content
SpringerLink
Log in

The Levi problem and the radius of convergence of holomorphic functions on metric vector 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. Aron, R., Entire functions of unbounded type on Banach spaces. Boll. Un. Mat. Ital. (4)9, 28–31 (1974).

    MathSciNet  MATH  Google Scholar 

  2. Bayoumi, A., Bounding subsets of some metric vector spaces. To appear in Arkiv for Mat. (1980).

    Google Scholar 

  3. Coeureé, G., Sur le rayon de bornologie des fonctions holomorphes. Sém. P. Lelong, Lecture Notes in Mathematics 578, 183–194. Springer-Verlag. 1977.

    Google Scholar 

  4. Dineen, S., Unbounded holomorphic functions on a Banach space. J. London Math. Soc. (24, 461–465 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  5. Gruman, L., Kiselman, C.O., Le problème de Levi dans les espaces de Banach à base. C.R. Acad. Sci. Paris, A 274, 1296–1299 (1972).

    MathSciNet  MATH  Google Scholar 

  6. Hörmander, L., An introduction to Complex Analysis in Several Variables. Princeton, Van Nostrand (1966).

    MATH  Google Scholar 

  7. Josefson, B., A counterexample to the Levi problem. In Proceedings on Infinite Dimensional Holomorphy. Lecture Notes in Mathematics 364, 168–177 (Springer 1974).

    Article  MathSciNet  MATH  Google Scholar 

  8. Kiselman, C.O., On the radius of convergence of an entire function in a normed space. Ann. Polon. Math. 33, 39–55 (1976).

    MathSciNet  MATH  Google Scholar 

  9. Kiselman, C.O., Geometric aspects of the theory of bounds for entire functions in normed spaces. In Infinite Dimensional Holomorphy and Applications. Ed. M.C. Matos, North-Holland, Amsterdam (1977).

    Google Scholar 

  10. Kiselman, C.O., Constructions de fonctions entières à rayon de convergence donné. Lecture Notes in Mathematics 578, 246–253. Springer-Verlag (1977).

    Article  MathSciNet  MATH  Google Scholar 

  11. Lelong, P., Fonctions plurisousharmoniques dans les espaces vectoriels topologiques. Lecture Notes in Mathematics 71, 167–190. Springer-Verlag 1968.

    Article  MathSciNet  MATH  Google Scholar 

  12. Nachbin, L., Topology on Spaces of Holomorphic Mappings. Springer-Verlag, Berlin, Heidelberg, New York (1969).

    Book  MATH  Google Scholar 

  13. Noverraz, P., Pseudoconvexité, convexité polynomiale et domaines d'holomorphie en dimension infinie. Amsterdam: North-Holland (1973).

    MATH  Google Scholar 

  14. Rolewicz, S., Metric Linear Spaces. Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (1972).

    Google Scholar 

  15. Schottenloher, M., Richness of the class of holomorphic functions on an infinite dimensional space. Functional Analysis, Results and Surveys. Conf. in Paderborn (1976). Amsterdam: North-Holland.

    Google Scholar 

  16. Schottenloher, M., Holomorphe Funktionen auf Gebieten über Banachräumen zu vorgegebenen Konvergenzradien. Manuscripta Math. 21, 315–327 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  17. Schottenloher, M., The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition. Ann. Inst. Fourier, Grenoble 26, 207–237 (1976).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Uppsala University, Thunbergsvägen 3, S - 752 38, Uppsala, Sweden

    Aboubakr Bayoumi

Authors
  1. Aboubakr Bayoumi
    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

Bayoumi, A. (1981). The Levi problem and the radius of convergence of holomorphic functions on metric vector 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/BFb0089267

Download citation

  • DOI: https://doi.org/10.1007/BFb0089267

  • 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