Holomorphic functions on fully nuclear spaces
Bulletin de la Société Mathématique de France, Volume 106 (1978), pp. 311-336.
@article{BSMF_1978__106__311_0,
     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},
     doi = {10.24033/bsmf.1875},
     mrnumber = {81b:46060},
     zbl = {0402.46017},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.1875/}
}
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
SP  - 311
EP  - 336
VL  - 106
PB  - Société mathématique de France
UR  - http://archive.numdam.org/articles/10.24033/bsmf.1875/
DO  - 10.24033/bsmf.1875
LA  - en
ID  - BSMF_1978__106__311_0
ER  - 
%0 Journal Article
%A Boland, Philip J.
%A Dineen, Seán
%T Holomorphic functions on fully nuclear spaces
%J Bulletin de la Société Mathématique de France
%D 1978
%P 311-336
%V 106
%I Société mathématique de France
%U http://archive.numdam.org/articles/10.24033/bsmf.1875/
%R 10.24033/bsmf.1875
%G en
%F BSMF_1978__106__311_0
Boland, Philip J.; Dineen, Seán. Holomorphic functions on fully nuclear spaces. Bulletin de la Société Mathématique de France, Volume 106 (1978), pp. 311-336. doi : 10.24033/bsmf.1875. http://archive.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

Cited by Sources: