Holomorphy types and spaces of entire functions of bounded type on Banach spaces

Fávaro, Vinícius V., and Jatobá, Ariosvaldo M.. "Holomorphy types and spaces of entire functions of bounded type on Banach spaces." Czechoslovak Mathematical Journal 59.4 (2009): 909-927. <http://eudml.org/doc/37966>.

@article{Fávaro2009,
abstract = {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.},
author = {Fávaro, Vinícius V., Jatobá, Ariosvaldo M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach spaces; holomorphy types; homogeneous polynomials; holomorphic functions; convolution operators; Borel transform; approximation and existence theorems; Banach space; holomorphy type; homogeneous polynomial; holomorphic function; convolution operator; Borel transform; approximation theorem; existence theorem},
language = {eng},
number = {4},
pages = {909-927},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Holomorphy types and spaces of entire functions of bounded type on Banach spaces},
url = {http://eudml.org/doc/37966},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Fávaro, Vinícius V.
AU - Jatobá, Ariosvaldo M.
TI - Holomorphy types and spaces of entire functions of bounded type on Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 909
EP - 927
AB - 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.
LA - eng
KW - Banach spaces; holomorphy types; homogeneous polynomials; holomorphic functions; convolution operators; Borel transform; approximation and existence theorems; Banach space; holomorphy type; homogeneous polynomial; holomorphic function; convolution operator; Borel transform; approximation theorem; existence theorem
UR - http://eudml.org/doc/37966
ER -