Abstract
In this paper spaces of entire functions of Θ-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 τ (p; q)-somantes e σ(p)-nucleares, Thesis, Universidade Estadual de Campinas, 2006.
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The first author is supported by Fapesp, project 07/50811-4. The second author is supported by CNPq.
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Fávaro, V.V., Jatobá, A.M. Holomorphy types and spaces of entire functions of bounded type on banach spaces. Czech Math J 59, 909–927 (2009). https://doi.org/10.1007/s10587-009-0063-x
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DOI: https://doi.org/10.1007/s10587-009-0063-x
Keywords
- Banach spaces
- holomorphy types
- homogeneous polynomials
- holomorphic functions
- convolution operators
- Borel transform
- approximation and existence theorems