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Start Over Subject approximation and existence theorems

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

Creator:
Fávaro, Vinícius V. and Jatobá, Ariosvaldo M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Banach spaces, holomorphy types, homogeneous polynomials, holomorphic functions, convolution operators, Borel transform, and approximation and existence theorems
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public