The Cartan-Thullen theorem for Banach spaces

Dineen, Seán

Annali della Scuola Normale Superiore di Pisa - Scienze Fisiche e Matematiche, Série 3, Tome 24 (1970) no. 4, pp. 667-676.

[1] Alexander, H., Analytic Functions on Banach spaces, Thesis, University of California at Berkeley, 1968.

[2] Bremermann, H.J., Holomorphic functionals and complex convexity in Banach spaces, Pacific J. of Math., 7 (1957), 811-831. | MR | Zbl

[3] Bremermann, H.J., Complex Convexity, Trans, Amer. Math. Soc., 82 (1956) 17-51. | MR | Zbl

[4] Cartan, Ii. and P. Thullen, Regularitäts - und Konvergenzbereiche, Math. Ann. 106 (1932) 617-647. | JFM | MR | Zbl

[5] Chae, S.B., Holomorphic germs on Banach spaces, University of Rochester, Thesis (1969).

[6] Coeuré, G., Fonction plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'étude des fonction analytiques, Thesis, Université de Nancy (1969).

[7] Dineen, S., Holomorphy types on a Banach space, University of Maryland, Thesis, (1969) (to be published in Studia Math.). | MR | Zbl

[8] Dineen, S., Unbounded holomorphic functions on a Banach space, (to be published in Jour. Lond. Math. Soc.). | Zbl

[9] Gupta, C.P., Malgrange theorem for nuclearly entire functions of bounded type on a Banach space, University of Rochester, Thesis (1966). Reproduced in Notas de Matematica Pura e Aplicada, Rio de Janeiro (1968). | MR | Zbl

[10] Gunning, R. and H. Rossi, Analytic functions of several complex variables, Prentice Hall, 1965. | MR | Zbl

[11] Hirschowitz, A., Remarques sur les ouverts d'holomorphie d'un produit dénombrable de droites., Annales de l'Institut Fourier, 19 (1969) 219-229. | Numdam | MR | Zbl

[12] Hirschowitz, A., Sur le non-plongement des varietes analytiques banachiques Réelles. C. R. Acad. Sc., Paris, 269 (844-846) 1969. | MR | Zbl

[13] Hörmander, L., An introduction to complex analysis in several variables, Van Nostrand, 1966. | MR | Zbl

[14] Horváth, J., Topological vector spaces and distributions, Vol. I, Addison-Wesley, 1966. | MR | Zbl

[15] Nachbin, L., Holomorphic functions, domains of holomorphy and local properties. Lecture notes at the University of Rochester, 1967, Prepared by R. M. Aron. | MR

[16] Nachbin, L., Thopology on spaces of holomorphic mappings. Ergebnisse der Matematik und ihre grenzgebiete 47. Springer-Verlag, Berlin (1969). | MR | Zbl

[17] Nachbin, L., Concerning holomorphy types for Banach spaces, Proceedings of the Colloqnium on Nuclear Spacer and Ideals in Operator Algebras held in Warsaw, Poland, (1969) (to be published in Studia Mathematica). | MR | Zbl

[18] Noverraz, P., Fonctions plurisousharmonique et analytiques dans les espaces vectoriels topologiques complexes, Thesis, Faculte des Sciences de Paris, 1969. | MR