Abstract
In this paper we present a general theory for holomorphic functions which is based on continuous convergence instead of topologies. The theory can be applied to locally convex spaces and bornological spaces.
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Aron, R., Schottenloher, M. Compact holomorphic mappings on Banach spaces and the approximation property. J. Funct. Anal.21 7–30 (1976).
Binz, E.: Continuous Convergence onC(X). Lect. Notes Math.469. Berlin-Heidelberg-New York: Springer. 1975.
Binz, E.: Notes on a characterization of function algebras. Math. Ann.186, 314–326 (1970).
Binz, E., Keller, H.H.: Funktionenräume in der Kategorie der Limesräume. Ann. Acad. Sci. Fenn. Ser. A I, Nr.383 (1966).
Bjon, S.: Eine ausgeglichene Limitierung auf Räumenn-linearer Abbildungen zwischen Limesvektorräumen. Soc. Sci. Fenn. Comment. Phys.-Math.43, 189–201 (1973).
Bjon, S.: Einbettbarkeit in den Bidualraum und Darstellbarkeit als projektiver Limes in Kategorien von Limesvektorräumen. Math. Nachr.97, 103–116 (1979).
Bjon, S.: On nuclear limit vector spaces. Categorical aspects of topology and analysis. Proc. Conf. Ottawa 1980, 27–39. Lect Notes Math.915. Berlin-Heidelberg-New York: Springer. 1982.
Butzmann, H.-P.: Über diec-Reflexivität vonC c (X). Comment. Math. Helv.47, 92–101 (1972).
Colombeau, J.F.: Differential Calculus and Holomorphy. Amsterdam-New York-Oxford: North-Holland. 1982.
Cook, C.H., Fischer, H.R.: On equicontinuity and continuous convergence. Math. Ann.159, 94–104 (1965).
Dineen, S.: Complex Analysis in Locally Convex Spaces. Amsterdam-New York-Oxford: North-Holland. 1981.
Fischer, H.R.: Limesräume. Math. Ann.137, 269–303 (1959).
Hogbe-Nlend, H.: Théorie des Bornologies et Applications. Lect. Notes Math.213. Berlin-Heidelberg-New York: Springer. 1971.
Jarchow, H.: Marinescu-Räume. Comment. Math. Helv.44, 138–163 (1969).
Keller, H.H.: Differential Calculus in Locally Convex Spaces. Lect. Notes Math.417. Berlin-Heidelberg-New York: Springer. 1974.
Lindström, M.: On Schwartz convergence vector spaces. Math. Nachr.117, 37–49 (1984).
Müller, B.:L c -undc-einbettbare Limesräume. Ann. Sc. Norm. Sup., Pisa, Cl. Sci., IV. Ser. 5, 509–526 (1978).
Schottenloher, M.: ε-product and continuation of analytic mappings. Analyse fonctionnelle et applications. C. r. Colloq. d'Analyse Rio de Janeiro 1972. pp. 261–270. Paris: Hermann 1975.
Schroder, M.: Marinescu structures andc-spaces. Convergence spaces. Proc. Conf. Reno 1976, pp. 204–235. Reno: Univ. Nevada 1976.
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Bjon, S., Lindström, M. A general approach to infinite-dimensional holomorphy. Monatshefte für Mathematik 101, 11–26 (1986). https://doi.org/10.1007/BF01326843
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DOI: https://doi.org/10.1007/BF01326843