Artículos de revistas
Reinhardt Domains Of Holomorphy In Banach Spaces
Registro en:
Advances In Mathematics. , v. 92, n. 2, p. 266 - 278, 1992.
18708
10.1016/0001-8708(92)90066-T
2-s2.0-38249012746
Autor
Matos M.C.
Nachbin L.
Institución
Resumen
It is known that in c0 the holomorphic functions representable by multiple power series (the series of monomials) are those of nuclear type. In this article we show that in a Banach space with unconditional Schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and, in fact, the domain of convergence of such a series. © 1992. 92 2 266 278 Boland, Dineen, Holomorphic functions on fully nuclear spaces (1978) Bull. Soc. Math. France, 106, pp. 311-336 Dineen, Analytic functionals on fully nuclear spaces (1982) Studia Math., 73, pp. 11-32 Dineen, Complex Analysis in Locally Convex Spaces (1981) Mathematics Studies, 57. , North-Holland, Amsterdam M. Fréchet, Une définition fonctionnelle de polynômes, Nouvelle Ann. Math.9, 145-162Fréchet, Sur les fonctionnelles continues (1910) Ann. Sci. École Norm. Dup., 27 (3), pp. 193-216 Fréchet, Sur les fonctionnelles bilinéaires (1915) Transactions of the American Mathematical Society, 16, pp. 215-234 Fréchet, Les transformations ponctuelles abstraites (1925) C. R. Acad. Sci. Paris, 180, pp. 1816-1817 Fréchet, Les polynômes abstraits (1929) J. Math. Pures Appl., 8 (9), pp. 71-92 Gâteaux, Sur les fonctionnelles continue et les fonctionnelles analytiques (1913) C. R. Acad. Sci. Paris, 157, pp. 325-327 Gâteaux, Fonctions d'une infinité des variables indépendantes (1919) Bull. Soc. Math. France, 47, pp. 70-96 Gâteaux, Sur diverses questions de calcul fonctionnel (1922) Bull. Soc. Math. France, 50, pp. 1-37 Graves, Topics in functional calculus (1935) Bulletin of the American Mathematical Society, 41, pp. 641-662 Gruman, Kiselman, Le problème de Levi dans les espaces de Banach à base (1972) C. R. Acad. Sci. París, 274, pp. 821-824 Hilbert, Wesen und Ziele einer Analysis der unendlich vielen unabhängigen Variabeln (1909) Rendiconti del Circolo Matematico di Palermo, 27, pp. 59-74 Hörmander, (1966) An Introduction to Complex Analysis in Several Variables, , Van Nostrand, Princeton, NJ Katz, Analytic Continuation in Infinite Dimension and Reinhardt Sets (1974) Doctoral Dissertation, , University of Rochester, Rochester, NY Littlewood, On bounded bilinear forms in an infinite number of variables (1930) The Quarterly Journal of Mathematics, 2, pp. 164-174 Martin, Contributions to the Theory of Functionals (1932) Doctoral Dissertation, , California Institute of Technology Matos, On Holomorphy in Banach Spaces and Absolute Convergence of Fourier Series (1985) Relatório Interno no 341, , IMECC-UNICAMP, Brazil (1988) Portugal. Math., 45 (4), pp. 429-450 Michal, Clifford, Fonctions analytiques implicites dans des espaces vectoriels abstraits (1933) C. R. Acad. Sci. Paris, 197, pp. 735-737 Mujica, Complex Analysis in Banach Spaces (1986) Mathematics Studies, 120. , North-Holland, Amsterdam Nachbin, Holomorphic Functions, Domains of Holomorphy and Local Properties (1970) Mathematics Studies, 1. , North-Holland, Amsterdam Nachbin, Topology on Spaces of Holomorphic Mappings (1969) Ergebnisse der Mathematik und ihrer Grenzgebiete, 47 Band. , Springer-Verlag, New York Pitt, A note on bilinear forms (1936) Journal of the London Mathematical Society, 11, pp. 174-180 Ryan, Holomorphic mappings on l1 (1987) Trans. Amer. Math. Soc., 302 (2), pp. 797-811 Taylor, Analytic functions in general analysis (1937) Ann. Scuola Norm. Sup. Pisa, 6 (2), pp. 277-292