ArticleOriginal scientific text
Title
Some remarks on holomorphic extension in infinite dimensions
Authors 1
Affiliations
- 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
- P. K. Ban, Banach hyperbolicity and the extension of holomorphic maps, Acta Math. Vietnam. 16 (1991), 187-200.
- T. J. Barth, Convex domains and Kobayashi hyperbolicity, Proc. Amer. Math. Soc. 79 (1980), 556-558.
- R. Brody, Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc. 235 (1978), 213-219.
- F. Docquier und H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123.
- 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.
- A. Hirschowitz, Prolongement analytique en dimension infinie, Ann. Inst. Fourier (Grenoble) 22 (2) (1972), 255-292.
- S. M. Ivashkovich, Hartogs' phenomenon for holomorphically convex Kähler manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 50 (1986), 866-873 (in Russian).
- S. Kobayashi, Hyperbolic Manifolds and Holomorphic Maps, Dekker, New York, 1970.
- P. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland Math. Stud. 3, North-Holland, Amsterdam, 1973.
- B. Shiffman, Extension of holomorphic maps into Hermitian manifolds, Math. Ann. 194 (1971), 249-258.
- B. D. Tac, Extending holomorphic maps in infinite dimensions, Ann. Polon. Math. 54 (1991), 241-253.
- D. D. Thai, On the D*-extension and the Hartogs extension, Ann. Scuola Norm. Sup. Pisa 18 (1991), 13-38.