We establish the equivalence between the weak holomorphicity and holomorphicity of Fréchet-valued functions on compact polydisks in (DFN)-spaces. Moreover, the relations between separately holomorphic functions and holomorphic functions on compact polydisks in (DFN)-spaces are also given.
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D. Vogt, “Frechtraume, zwischen denen jede stetige linear Abbildung beschraukt ist,” J. Reine Angew. Math., 345, 182–200 (1983).
D. Vogt, “On two classes of (F)-spaces,” Arch. Math., 45, 255–266 (1985).
D. Vogt, “Some results on continuous linear maps between Fréchet spaces,” in: K.-D. Bierstedt and B. Fuchssteiner (editors), Functional Analysis: Surveys and Recent Results. III, North-Holland, Amsterdam (1984), pp. 349–381.
S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland, Amsterdam (1981).
A. Pietsch, Nuclear Locally Convex Spaces, Springer, Berlin (1972).
Phan Thien Danh and Nguyen Van Khue, “Structure of space of germs holomorphic functions,” Publ. Mat., 41, 467–480 (1997).
Le Mau Hai, “Weak extensions of Fréchet-valued holomorphic functions on compact sets and linear topological invariants,” Acta. Math. Vietnamica, 21, No. 2, 183–199 (1996).
Nguyen Van Khue and Bui Dac Tac, “Extending holomorphic maps from compact sets in infinite dimension,” Stud. Math., 45, 263–272 (1990).
J. Siciak, “Weak analytic continuation from compact sets of \(\mathbb{C}^{n}\),” Lect. Notes Math., 364, 92–96 (1974).
L. Waelbroeck, “Weak analytic functions and the closed graph theorem,” Lect. Notes Math., 364, 97–100 (1974).
R. Meise and D. Vogt, Introduction to Functional Analysis, Clarendon Press, Oxford (1997).
P. J. Boland and S. Dineen, “Holomorphic functions on fully nuclear spaces,” Bull. Soc. Math. France, 106, 311–336 (1978).
Le Mau Hai, “Meromorphic functions of uniform type and linear topological invariants,” Vietnam J. Math., 23, 145–161 (1995).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 11, pp. 1578–1584, November, 2008.
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Hien Bang, P. Fréchet-valued holomorphic functions on compact sets in (DFN)-spaces. Ukr Math J 60, 1852–1859 (2008). https://doi.org/10.1007/s11253-009-0175-3
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DOI: https://doi.org/10.1007/s11253-009-0175-3