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.
@article{bwmeta1.element.bwnjournal-article-apmv54z3p241bwm,
author = {Bui Dac Tac},
title = {Extending holomorphic maps in infinite dimensions},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {241-253},
zbl = {0736.46042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p241bwm}
}
Bui Dac Tac. Extending holomorphic maps in infinite dimensions. Annales Polonici Mathematici, Tome 55 (1991) pp. 241-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p241bwm/
[000] [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. | Zbl 0237.32008
[001] [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.
[002] [3] G. Coeuré, Analytic Functions and Manifolds in Infinite Dimensional Spaces, North-Holland Math. Stud. 11, 1974. | Zbl 0282.32015
[003] [4] F. Docquier und H. Grauert, Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann. 140 (1960), 94-123. | Zbl 0095.28004
[004] [5] A. Hirschowitz, Prolongement analytique en dimension infinie, Ann. Inst. Fourier (Grenoble) 22 (2) (1972), 255-292. | Zbl 0224.32015
[005] [6] A. Hirschowitz, Domaines de Stein et fonctions holomorphes bornées, Math. Ann. 213 (1975), 185-193. | Zbl 0284.32011
[006] [7] S. M. Ivashkovich, Hartogs' phenomenon for holomorphically convex Kähler manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 50 (4) (1986) 866-873.
[007] [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.
[008] [9] L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Gos. Izdat. Fiz.-Mat. Liter., Moscow 1959 (in Russian). | Zbl 0127.06102
[009] [10] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York 1970. | Zbl 0207.37902
[010] [11] E. Ligocka and J. Siciak, Weak analytic continuation, Bull. Acad. Pol. Sci. Sér. Sci. Math. Astronom. Phys. 20 (6) (1972), 461-466. | Zbl 0241.46013
[011] [12] P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, 1984.
[012] [13] P. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomor- phie en Dimension Infinie, North-Holland Math. Stud. 3, 1973. | Zbl 0251.46049
[013] [14] M. Schottenloher, Analytic continuation and regular classes in locally convex Hausdorff spaces, Portugal. Math. 33 (4) (1974), 219-250. | Zbl 0293.32023
[014] [15] M. Schottenloher, The Levi problem for domains spread over locally convex spaces, Ann. Inst. Fourier (Grenoble) 26 (1976), 255-292.
[015] [16] B. Shiffman, Extension of holomorphic maps into Hermitian manifolds, Math. Ann. 194 (1971), 249-258. | Zbl 0213.36001
[016] [17] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math. 29 (1975), 205-230. | Zbl 0333.32011