Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The convergence-extension theorem of Noguchi in infinite dimensions

Authors: Do Duc Thai and Tran Ngoc Giao
Journal: Proc. Amer. Math. Soc. 130 (2002), 477-482
MSC (1991): Primary 32H05, 32H15; Secondary 32M05, 32M99
Published electronically: September 19, 2001
MathSciNet review: 1862128
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we give generalizations of Noguchi's convergence-extension theorem to the case of infinite dimension.

References [Enhancements On Off] (What's this?)

  • [J-K] J.E. Joseph and M.H. Kwack, Hyperbolic embedding and spaces of continuous extensions of holomorphic maps, J. Geom. Analysis 4(1994), 361-378. MR 95g:32037
  • [Ko] S.Kobayashi, Hyperbolic Complex Spaces, vol. 318(1998), Grundlehren der mathematischen Wissenschaften. MR 99m:32026
  • [La] S. Lang, Introduction to Complex Hyperbolic Spaces, Springer-Verlag (1987). MR 88f:32065
  • [Ma] P. Mazet, Analytic Sets in Locally Convex Spaces, Math. Studies, North-Holland, v.121(1987). 1984 edition MR 86i:32012
  • [Mu] J. Mujica, Complex Analysis in Banach Spaces, Math. Studies, North-Holland, v.120(1986). MR 88d:46084
  • [No] J. Noguchi, Moduli spaces of holomorphic mappings into hyperbolically imbedded complex spaces and locally symmetric spaces, Invent. Math. 93(1988), 15-34. MR 89j:32031
  • [N-O] J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, Translations of Math. Monographs, Amer. Math. Soc., v. 80(1990). MR 92e:32001
  • [Ra] J. P. Ramis, Sous-ensembles Analytiques d'une Variété Banachique Complexe, Springer-Verlag (1970). MR 45:2205
  • [T-H] Do Duc Thai and Nguyen Le Huong, On the disc-convexity of Banach analytic manifolds, Ann. Pol. Math. 69(1998), 1-11. MR 2000b:32042
  • [V-F] E. Vesentini and T. Franzoni, Holomorphic Maps and Invariant Distances, Math. Studies, North-Holland, v. 40(1980). MR 82a:32032
  • [Ve] E. Vesentini, Invariant distances and invariant differential metric in locally convex spaces, Spectral theory, Banach Centre Publication U.8 P.W.N, Polish Sci. Publisher Warsaw, (1982), 493-512. MR 85d:32049

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32H05, 32H15, 32M05, 32M99

Retrieve articles in all journals with MSC (1991): 32H05, 32H15, 32M05, 32M99

Additional Information

Do Duc Thai
Affiliation: Department of Mathematics, Pedagogical University of Hanoi, Caugiay, Hanoi, Vietnam
Address at time of publication: Department of Mathematics, Hanoi University of Education, Cau Giay, Tu Liem, Hanoi, Vietnam

Tran Ngoc Giao
Affiliation: Department of Mathematics, Pedagogical University of Vinh, Vinh, Vietnam

Keywords: Banach analytic space, complex hypersurface of a Banach analytic manifold with only normal crossings, hyperbolically imbedded Banach analytic subspace of a Banach analytic space
Received by editor(s): June 27, 2000
Published electronically: September 19, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society