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ArticleOriginal scientific text

Title

Extending holomorphic maps in infinite dimensions

Authors 1

Affiliations

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

Abstract

Studying the sequential completeness of the space of germs of Banach-valued holomorphic functions at a points of a metric vector space some theorems on extension of holomorphic maps on Riemann domains over topological vector spaces with values in some locally convex analytic spaces are proved. Moreover, the extendability of holomorphic maps with values in complete C-spaces to the envelope of holomorphy for the class of bounded holomorphic functions is also established. These results are known in some special cases.

Bibliography

  1. K. Adachi, M. Suzuki and M. Yoshida, Continuation of holomorphic mappings, with values in a complex Lie group, Pacific J. Math. 47 (1) (1973), 1-4.
  2. A. Bayoumi, The Levi problem and the radius of convergence of holomorphic functions on metric vector spaces, in: Lecture Notes in Math. 843, Springer, 1981, 9-32.
  3. G. Coeuré, Analytic Functions and Manifolds in Infinite Dimensional Spaces, North-Holland Math. Stud. 11, 1974.
  4. F. Docquier und H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123.
  5. A. Hirschowitz, Prolongement analytique en dimension infinie, Ann. Inst. Fourier (Grenoble) 22 (2) (1972), 255-292.
  6. A. Hirschowitz, Domaines de Stein et fonctions holomorphes bornées, Math. Ann. 213 (1975), 185-193.
  7. S. M. Ivashkovich, Hartogs' phenomenon for holomorphically convex Kähler manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 50 (4) (1986) 866-873.
  8. B. Josefson, A counter-example in the Levi problem, in: Proceedings on Infinite Dimensional Holomorphy, Lecture Notes in Math. 364, Springer, 1974, 168-177.
  9. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Gos. Izdat. Fiz.-Mat. Liter., Moscow 1959 (in Russian).
  10. S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York 1970.
  11. E. Ligocka and J. Siciak, Weak analytic continuation, Bull. Acad. Pol. Sci. Sér. Sci. Math. Astronom. Phys. 20 (6) (1972), 461-466.
  12. P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, 1984.
  13. P. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomor- phie en Dimension Infinie, North-Holland Math. Stud. 3, 1973.
  14. M. Schottenloher, Analytic continuation and regular classes in locally convex Hausdorff spaces, Portugal. Math. 33 (4) (1974), 219-250.
  15. M. Schottenloher, The Levi problem for domains spread over locally convex spaces, Ann. Inst. Fourier (Grenoble) 26 (1976), 255-292.
  16. B. Shiffman, Extension of holomorphic maps into Hermitian manifolds, Math. Ann. 194 (1971), 249-258.
  17. N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230.
Annales Polonici Mathematici
1991/54/3
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Pages:
241-253
Main language of publication
English
Received
1988-11-05
Accepted
1989-08-03
Published
1991
Exact and natural sciences