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Holomorphic functions on strict inductive limits

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Abstract

We study strict inductive limits of Fréchet Montel (FM) spaces and reflexive Fréchet (RF) spaces and we obtain some interesting examples in the theory of infinite dimensional holomorphy.

PM(kE′) and PHY(kE′) will denote respectively the set of all k-homogeneous polynomials on E′ that are bounded on bounded sets and the set of all k-homogeneous polynomials on E′ that are continuous on compact sets. ℒSM(kE′) is the space of all symetric k -multilinear mappings from E′ × ... × E′ into C that are bounded on bounded sets.

HHY(E′) will denote the set of all G-analytic functions on E′ that are continuous on the compact subsets of E′.

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References

  1. J. A. Barroso, M. C. Matos and L. Nachbin, On bounded sets of holomorphic mappings, Proceedings on Infinite Dimensional Holomorphy, University of Kentucky (1973), Springer Verlag Lecture Notes in Mathematics, Vol. 364, p. 123–134, 1974.

    MathSciNet  Google Scholar 

  2. P. J. Boland and S. Dineen, Duality Theory for Spaces of Germs and Holomorphic Functions on Nuclear Spaces, Advances in Holomorphy, Ed. J. A. Barroso, North-Holland, 1979, p. 179-207.

  3. P. J. Boland and S. Dineen, Holomorphic Functions on Fully Nuclear Spaces, Bull. Soc. Math. France, 106, p. 311–336, 1978.

    MathSciNet  MATH  Google Scholar 

  4. S. Dineen, Surjective Limits of Locally Convex Spaces and their application to Infinite Dimension Holomorphy, Bull. Soc. Math. France, 103, p. 441–509, 1975.

    MathSciNet  MATH  Google Scholar 

  5. S. Dineen, Holomorphic Functions on Strong Duals of Fréchet — Montel Spaces, Infinite Dimensional Holomorphy and Applications, North Holland Mathematical Studies no. 12, p. 147-166, 1977.

  6. S. Dineen, Holomorphic Functions on Locally Convex Topological Vector Spaces: 1. Locally Convex Topologies on H(U), Ann. Inst. Fourier, Grenoble, 23, 1. p. 19–54 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Dineen, Complex Analysis on Locally Convex Spaces, to appear.

  8. N.J. Kalton, Normalization Properties of Schauder Bases, Offprint from Proceedings of the London Mathematical Society, Third Series, Volume XXII, Febr. 1971, p. 91-105.

  9. M. Schottenloher, ϵ-product and Continuation of Analytic Mapping, Analyse Fonctionnelle and Applications, Ed. L. Nachbin, Hermann, 1975, p. 261-270.

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  1. Instituto de Matematica, Universidade Federal do Rio de Janeiro, Caixa Postal 1835, 21910, Rio de Janeiro, Brasil

    Luiza A. Moraes

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  1. Luiza A. Moraes
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Moraes, L.A. Holomorphic functions on strict inductive limits. Results. Math. 4, 201–212 (1981). https://doi.org/10.1007/BF03322978

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