Holomorphic functions on fully nuclear spaces
Bulletin de la Société Mathématique de France, Tome 106 (1978), pp. 311-336. 
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     author = {Boland, Philip J. and Dineen, Se\'an},
     title = {Holomorphic functions on fully nuclear spaces},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {311--336},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {106},
     year = {1978},
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     zbl = {0402.46017},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.1875/}
}
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Boland, Philip J.; Dineen, Seán. Holomorphic functions on fully nuclear spaces. Bulletin de la Société Mathématique de France, Tome 106 (1978), pp. 311-336. doi : 10.24033/bsmf.1875. https://www.numdam.org/articles/10.24033/bsmf.1875/

[1] Barroso (J. A.). - Topologias nos espaços de aplicacoes holomorfas entre espaços localmente convexos, Anais. Acad. Bras. Ciencias, t. 43, 1971, p. 527-546. | MR | Zbl

[2] Barroso (J. A.), Matos (M. C.), Nachbin (L.). - On bounded sets of holomorphic mappings, "Proceedings on infinite dimensional holomorphy", University of Kentucky, 1973", p. 123-133. - Berlin, Springer-Verlag, 1974 (Lecture Notes in Mathematics, 364). | MR | Zbl

[3] Barroso (J. A.), Nachbin (L.). - τ = τω for domains in CN (preprint).

[4] Bierstedt (K. D.), Meise (R.). - Nuclearity and the Schwartz property in the theory of holomorphic functions on metrizable locally convex spaces, "Infinite dimensional holomorphy and applications [1975 São Paulo]", p. 93-129. - Amsterdam, North-Holland publishing Company, 1977 (North-Holland Mathematics Studies, 12 ; Notas de Matematica, 54). | MR | Zbl

[5] Bierstedt (K. D.), Meise (R.). - H (K) et (H (U), τω) sur des espaces métrisables nucléaires ou de Schwartz, C.R. Acad. Sc. Paris, t. 283, série A, 1976, p. 325-327. | MR | Zbl

[6] Boland (P. J.). - Malgrange theorem for entire functions on nuclear spaces, "Proceedings on infinite dimensional holomorphy, University of Kentucky 1973", p. 135-144. - Berlin, Springer-Verlag, 1974 (Lecture Notes in Mathematics, 364). | MR | Zbl

[7] Boland (P. J.). - Holomorphic functions on nuclear spaces, Trans. Amer. math. Soc., t. 209, 1975, p. 275-281. | MR | Zbl

[8] Boland (P. J.). - An example of a nuclear space in infinite dimensional holomorphy, Arkiv för Matematik, t. 15, 1977, p. 87-91. | MR | Zbl

[9] Boland (P. J.). - Duality and spaces of holomorphic functions, "Infinite dimensional holomorphy and applications [1975. São Paulo]", p. 131-138. - Amsterdam, North-Holland publishing Company, 1977 (North-Holland Mathematics Studies, 12 ; Notas de Matematica, 54). | MR | Zbl

[10] Dineen (S.). - Holomorphic functions on locally convex topological vector spaces, I : Locally convex topologies on ℋ (U), Ann. Inst. Fourier, Grenoble, t. 23, 1973, fasc. 1, p. 19-54. | Numdam | MR | Zbl

[11] Dineen (S.). - Surjective limits of locally convex spaces and their applications to infinite dimensional holomorphy, Bull. Soc. math. France, t. 103, 1975, p. 441-509. | Numdam | MR | Zbl

[12] Dineen (S.). - Holomorphic functions on strong duals of Fréchet-Montel spaces, "Infinite dimensional holomorphy and applications [1975. São Paulo]", p. 147-166. - Amsterdam, North-Holland publishing Company, 1977 (North-Holland Mathematics Studies, 12 ; Notas de Matematica, 54). | MR | Zbl

[13] Dineen (S.). - Holomorphic functions and surjective limits, "Proceedings on infinite dimensional holomorphy, University of Kentucky, 1973", p. 1-12. - Berlin, Springer-Verlag, 1974 (Lecture Notes in Mathematics, 364). | MR | Zbl

[14] Grothendieck (A.). - Produits tensoriels topologiques et espaces nucléaires. - Providence, American mathematical Society, 1955 (Memoirs of the American mathematical Society, 16). | MR | Zbl

[15] Horvath (J.). - Topological vector spaces and distributions, Vol. I. - Reading. Addison-Wesley publishing Company, 1966 (Addison-Wesley Series in Mathematics). | MR | Zbl

[16] Jarchow (H.). - Nuclear locally convex spaces. - [College Park], University of Maryland, Department of Mathematics, 1976 (University of Maryland Lecture Notes, 13). | MR

[17] Katz (G. I.). - Analytic continuation in infinite dimensions and Reinhardt sets, Thesis, University of Rochester, 1974.

[18] Kelly (J. L.). - General topology. - New York, D. Van Nostrand publishing Company, 1955 (University Series in higher Mathematics). | Zbl

[19] Köthe (G.). - Topological vector spaces, Vol. I - Berlin, Springer-Verlag, 1969 (Grundlehren der mathematischen Wissenschaften, 159). | Zbl

[20] Mujica (J.). - Spaces of germs of holomorphic functions, Advances in Mathematics (to appear). | Zbl

[21] Nachbin (L.). - Topology on spaces of holomorphic mappings. - Berlin, Springer-Verlag, 1969 (Ergebnisse der Mathematik, 47). | MR | Zbl

[22] Noverraz (P.). - Pseudo-convexité, convexité polynomiale et domaines d'holomorphie en dimension infinie. - Amsterdam, North-Holland publishing Company, 1973 (North-Holland Mathematics Studies, 3 ; Notas de Matematicas, 48). | MR | Zbl

[23] Pietsch (A.). - Nuclear locally convex spaces. 2nd edition. - Berlin, Springer-Verlag, 1972 (Ergebnisse der Mathematik, 66). | MR | Zbl

[24] Schottenloher (M.). - τω = τ0 for domains in CN (preprint).

[25] Waelbroeck (L.). - The nuclearity of ATT (U), "Infinite dimensional holomorphy and applications [1975. Sao Paulo]", p. 425-435. - Amsterdam, North-Holland publishing Company, 1977 (North-Holland Mathematics Studies, 12 ; Notas de Matematica, 54). | MR | Zbl

  • Fávaro, V. V.; Mujica, J. Convolution operators on spaces of entire functions, Mathematische Nachrichten, Volume 291 (2018) no. 1, p. 41 | DOI:10.1002/mana.201600247
  • Quang, Thai Thuan; Van Dai, Nguyen On the Holomorphic Extension of Vector Valued Functions, Complex Analysis and Operator Theory, Volume 9 (2015) no. 3, p. 567 | DOI:10.1007/s11785-014-0382-2
  • Coates, Tom; Iritani, Hiroshi On the convergence of Gromov-Witten potentials and Givental's formula, Michigan Mathematical Journal, Volume 64 (2015) no. 3 | DOI:10.1307/mmj/1441116660
  • Quang, Thai Thuan Weakly and Separately Holomorphic Functions on Compact Determining Polydiscs in (DFN)-Spaces, Complex Analysis and Operator Theory, Volume 7 (2013) no. 5, p. 1437 | DOI:10.1007/s11785-011-0194-6
  • Defant, Andreas; Maestre, Manuel; Prengel, Christopher Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009 (2009) no. 634 | DOI:10.1515/crelle.2009.068
  • Hien Bang, Pham Fréchet-valued holomorphic functions on compact sets in (DFN)-spaces, Ukrainian Mathematical Journal, Volume 60 (2008) no. 11, p. 1852 | DOI:10.1007/s11253-009-0175-3
  • Defant, Andreas; Díaz, Juan Carlos; García, Domingo; Maestre, Manuel Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions, Mathematische Nachrichten, Volume 233-234 (2002) no. 1, p. 89 | DOI:10.1002/1522-2616(200201)233:1<89::aid-mana89>3.0.co;2-y
  • Dineen, Seán; Galindo, Pablo; García, Domingo; Maestre, Manuel Linearization of holomorphic mappings on fully nuclear spaces with a basis, Glasgow Mathematical Journal, Volume 36 (1994) no. 2, p. 201 | DOI:10.1017/s0017089500030743
  • Matos, Mário C; Nachbin, Leopoldo Reinhardt domains of holomorphy in Banach spaces, Advances in Mathematics, Volume 92 (1992) no. 2, p. 266 | DOI:10.1016/0001-8708(92)90066-t
  • Defant, Andreas; Moraes, Luiza A. On unconditional bases in spaces of holomorphic functions in infinite dimensions, Archiv der Mathematik, Volume 56 (1991) no. 2, p. 163 | DOI:10.1007/bf01200347
  • Ansemil, J. M. Relations between τ0 and τω on Spaces of Holomorphic Functions, Advances in the Theory of Fréchet Spaces (1989), p. 173 | DOI:10.1007/978-94-009-2456-7_10
  • Bjon, Sten; Lindström, Mikael Algebras of holomorphic functions, Journal of Mathematical Analysis and Applications, Volume 128 (1987) no. 1, p. 207 | DOI:10.1016/0022-247x(87)90226-5
  • Ryan, Raymond A. Holomorphic mappings on 𝑙₁, Transactions of the American Mathematical Society, Volume 302 (1987) no. 2, p. 797 | DOI:10.1090/s0002-9947-1987-0891648-7
  • Mujica, Jorge Polynomial Approximation in Nuclear Fréchet Spaces, Aspects of Mathematics and its Applications, Volume 34 (1986), p. 601 | DOI:10.1016/s0924-6509(09)70283-1
  • Mujica, Jorge A Banach-Dieudonné theorem for germs of holomorphic functions, Journal of Functional Analysis, Volume 57 (1984) no. 1, p. 31 | DOI:10.1016/0022-1236(84)90099-5
  • Meise, Reinhold; Vogt, Dietmar Counterexamples in holomorphic functions on nuclear Fr�chet spaces, Mathematische Zeitschrift, Volume 182 (1983) no. 2, p. 167 | DOI:10.1007/bf01175619
  • Benndorf, Andreas On bounded approximation properties of spaces of holomorphic functions on certain open subsets of strong duals of nuclear Fr�chet spaces, Archiv der Mathematik, Volume 38 (1982) no. 1, p. 248 | DOI:10.1007/bf01304784
  • Bibliography, Differential Calculus and Holomorphy - Real and complex analysis in locally convex spaces, Volume 64 (1982), p. 431 | DOI:10.1016/s0304-0208(08)73536-9
  • Meise, Reinhold G.; Vogt, Dietmar An Interpretation of TΩ and Tδ as Normal Topologies of Sequence Spaces, Functional Analysis, Holomorphy and Approximation Theory, Proceedings of the Seminario de Analise Functional, Holomorfia e Teoria da Aproximaçāo, Volume 71 (1982), p. 273 | DOI:10.1016/s0304-0208(08)72539-8
  • Börgens, M.; Meise, R.; Vogt, D. ∧(α)-nuclearity in infinite dimensional holomorphy, Mathematische Nachrichten, Volume 106 (1982) no. 1, p. 129 | DOI:10.1002/mana.19821060113
  • Schottenloher, Martin Michael problem and algebras of holomorphic functions, Archiv der Mathematik, Volume 37 (1981) no. 1, p. 241 | DOI:10.1007/bf01234351
  • Moraes, Luiza A. Holomorphic functions on strict inductive limits, Results in Mathematics, Volume 4 (1981) no. 1-2, p. 201 | DOI:10.1007/bf03322978
  • Dineen, Seán Holomorphic Functions on Nuclear Sequence Spaces, Functional Analysis: Surveys and Recent Results II, Volume 38 (1980), p. 239 | DOI:10.1016/s0304-0208(08)70810-7

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