Geodesic
Holomorphy types and spaces of entire functions of bounded type on Banach spaces
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 909-927 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper spaces of entire functions of $\Theta $-holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we ``construct an algorithm'' to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions. Annales de l'Institute Fourier (Grenoble) VI, 1955/56, 271--355; C. Gupta: Convolution Operators and Holomorphic Mappings on a Banach Space, Séminaire d'Analyse Moderne, 2, Université de Sherbrooke, Sherbrooke, 1969; M. Matos: Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, 2007; and X. Mujica: Aplicações $\tau (p;q)$-somantes e $\sigma (p)$-nucleares, Thesis, Universidade Estadual de Campinas, 2006.
In this paper spaces of entire functions of $\Theta $-holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we ``construct an algorithm'' to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions. Annales de l'Institute Fourier (Grenoble) VI, 1955/56, 271--355; C. Gupta: Convolution Operators and Holomorphic Mappings on a Banach Space, Séminaire d'Analyse Moderne, 2, Université de Sherbrooke, Sherbrooke, 1969; M. Matos: Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, 2007; and X. Mujica: Aplicações $\tau (p;q)$-somantes e $\sigma (p)$-nucleares, Thesis, Universidade Estadual de Campinas, 2006.
Classification : 46E50, 46G20, 46G25, 47B38
Keywords: Banach spaces; holomorphy types; homogeneous polynomials; holomorphic functions; convolution operators; Borel transform; approximation and existence theorems 
@article{CMJ_2009_59_4_a3,
     author = {F\'avaro, Vin{\'\i}cius V. and Jatob\'a, Ariosvaldo M.},
     title = {Holomorphy types and spaces of entire functions of bounded type on {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {909--927},
     year = {2009},
     volume = {59},
     number = {4},
     mrnumber = {2563566},
     zbl = {1224.46087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a3/}
}
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Fávaro, Vinícius V.; Jatobá, Ariosvaldo M. Holomorphy types and spaces of entire functions of bounded type on Banach spaces. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 909-927. http://geodesic.mathdoc.fr/item/CMJ_2009_59_4_a3/