Holomorphic functions on fully nuclear spaces
Bulletin de la Société Mathématique de France (1978)
- Volume: 106, page 311-336
- ISSN: 0037-9484
Access Full Article
topHow to cite
topBoland, Philip J., and Dineen, Seán. "Holomorphic functions on fully nuclear spaces." Bulletin de la Société Mathématique de France 106 (1978): 311-336. <http://eudml.org/doc/87330>.
@article{Boland1978,
author = {Boland, Philip J., Dineen, Seán},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Holomorphic Functions on Nuclear Spaces; Fully Nuclear Space; Equicontinuous Basis; Uniform Convergence on Compact Subsets; Compact Ported Topology; Topological Dual; Holomorphic Germs; Inductive Limit Of Banach Spaces},
language = {eng},
pages = {311-336},
publisher = {Société mathématique de France},
title = {Holomorphic functions on fully nuclear spaces},
url = {http://eudml.org/doc/87330},
volume = {106},
year = {1978},
}
TY - JOUR
AU - Boland, Philip J.
AU - Dineen, Seán
TI - Holomorphic functions on fully nuclear spaces
JO - Bulletin de la Société Mathématique de France
PY - 1978
PB - Société mathématique de France
VL - 106
SP - 311
EP - 336
LA - eng
KW - Holomorphic Functions on Nuclear Spaces; Fully Nuclear Space; Equicontinuous Basis; Uniform Convergence on Compact Subsets; Compact Ported Topology; Topological Dual; Holomorphic Germs; Inductive Limit Of Banach Spaces
UR - http://eudml.org/doc/87330
ER -
References
top- [1] BARROSO (J. A.). — Topologias nos espaços de aplicacoes holomorfas entre espaços localmente convexos, Anais. Acad. Bras. Ciencias, t. 43, 1971, p. 527-546. Zbl0246.46012MR46 #7874
- [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). Zbl0282.46032MR52 #15003
- [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). Zbl0373.46054MR58 #30236
- [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. Zbl0341.46028MR58 #2275
- [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). Zbl0282.46019MR54 #8285
- [7] BOLAND (P. J.). — Holomorphic functions on nuclear spaces, Trans. Amer. math. Soc., t. 209, 1975, p. 275-281. Zbl0317.46036MR52 #8931
- [8] BOLAND (P. J.). — An example of a nuclear space in infinite dimensional holomorphy, Arkiv för Matematik, t. 15, 1977, p. 87-91. Zbl0348.46035MR56 #9263
- [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). Zbl0372.46026MR58 #12359
- [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. Zbl0241.46022MR58 #17843
- [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. Zbl0328.46045MR54 #11058
- [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). Zbl0379.46039MR58 #12360
- [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). Zbl0277.46006MR54 #11057
- [14] GROTHENDIECK (A.). — Produits tensoriels topologiques et espaces nucléaires. - Providence, American mathematical Society, 1955 (Memoirs of the American mathematical Society, 16). Zbl0064.35501MR17,763c
- [15] HORVATH (J.). — Topological vector spaces and distributions, Vol. I. - Reading. Addison-Wesley publishing Company, 1966 (Addison-Wesley Series in Mathematics). Zbl0143.15101MR34 #4863
- [16] JARCHOW (H.). — Nuclear locally convex spaces. - [College Park], University of Maryland, Department of Mathematics, 1976 (University of Maryland Lecture Notes, 13). MR57 #1066
- [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). Zbl0066.16604
- [19] KÖTHE (G.). — Topological vector spaces, Vol. I - Berlin, Springer-Verlag, 1969 (Grundlehren der mathematischen Wissenschaften, 159). Zbl0179.17001
- [20] MUJICA (J.). — Spaces of germs of holomorphic functions, Advances in Mathematics (to appear). Zbl0489.46020
- [21] NACHBIN (L.). — Topology on spaces of holomorphic mappings. - Berlin, Springer-Verlag, 1969 (Ergebnisse der Mathematik, 47). Zbl0172.39902MR40 #7787
- [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). Zbl0251.46049MR50 #10814
- [23] PIETSCH (A.). — Nuclear locally convex spaces. 2nd edition. - Berlin, Springer-Verlag, 1972 (Ergebnisse der Mathematik, 66). Zbl0236.46001MR50 #2853
- [24] SCHOTTENLOHER (M.). — τω = τ0 for domains in CN (preprint).
- [25] WAELBROECK (L.). — The nuclearity of (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). Zbl0439.46017MR58 #30237
Citations in EuDML Documents
top- Philipp J. Boland, Polynomials and multilinear forms on fully nuclear spaces
- Manfred Scheve, Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces
- Christopher Boyd, Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces
- Seán Dineen, Reinhold Meise, Dietmar Vogt, Characterization of nuclear Fréchet spaces in which every bounded set is polar
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.