ArticleOriginal scientific text

Title

Some remarks on holomorphic extension in infinite dimensions

Authors 1

Affiliations

  1. Department of Mathematics, Pedagogical Institute Hanoi, I Hanoi, Vietnam

Abstract

In finite-dimensional complex analysis, the extension of holomorphic maps has been investigated by many authors. In recent years some authors have considered this problem in the infinite-dimensional case. The aim of the present note is to study the extension of holomorphic maps with values in some Banach complex manifolds.

Bibliography

  1. P. K. Ban, Banach hyperbolicity and the extension of holomorphic maps, Acta Math. Vietnam. 16 (1991), 187-200.
  2. T. J. Barth, Convex domains and Kobayashi hyperbolicity, Proc. Amer. Math. Soc. 79 (1980), 556-558.
  3. R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213-219.
  4. F. Docquier und H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123.
  5. L. Gruman et C. O. Kiselman, Le problème de Levi dans les espaces de Banach à base, C. R. Acad. Sci. Paris Sér. A 274 (1972), 1296-1298.
  6. A. Hirschowitz, Prolongement analytique en dimension infinie, Ann. Inst. Fourier (Grenoble) 22 (2) (1972), 255-292.
  7. S. M. Ivashkovich, Hartogs' phenomenon for holomorphically convex Kähler manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), 866-873 (in Russian).
  8. S. Kobayashi, Hyperbolic Manifolds and Holomorphic Maps, Dekker, New York, 1970.
  9. P. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland Math. Stud. 3, North-Holland, Amsterdam, 1973.
  10. B. Shiffman, Extension of holomorphic maps into Hermitian manifolds, Math. Ann. 194 (1971), 249-258.
  11. B. D. Tac, Extending holomorphic maps in infinite dimensions, Ann. Polon. Math. 54 (1991), 241-253.
  12. D. D. Thai, On the D*-extension and the Hartogs extension, Ann. Scuola Norm. Sup. Pisa 18 (1991), 13-38.
Pages:
155-159
Main language of publication
English
Received
1992-08-05
Published
1994
Exact and natural sciences