Holomorphy types on a Banach spaces / Tipos de holomorfia em espaços de Banach




In this work we introduce and study functions of ?-holomorphy type of bounded type. In particular we obtain a duality result via the Borel transform and we prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to C. Gupta [21], M. Matos [28] and X. Mujica [32]. We study the relationships among the space Hb(E; F) of entire mappings of bounded type, the space HNb(E; F) of entire mappings of nuclear bounded type, the space HPIb(E; F) of entire mappings of Pietsch integral bounded type, and the space HGIb(E; F) of entire mappings of Grothendieck integral bounded type. We extend to the case of entire mappings several results due to R. Alencar [2] and R. Cilia and J. Gutiérrez [10] in the case of homogeneous polynomials


holomorphic functions banach spaces convolution operators operadores de convolução borel transform espaços de transformada de borel banach funções holomorfas

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