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Holomorphy types and spaces of entire functions of bounded type on Banach spaces. (English) Zbl 1224.46087

Summary: 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 [Ann. Inst. Fourier 6, 271–355 (1955/56; Zbl 0071.09002)], C. P. Gupta [Convolution operators and holomorphic mappings on a Banach space. Seminaire d’analyse moderne. No.2. Sherbrooke, Quebec, Canada: Departement de Mathematiques, Universite de Sherbrooke (1969; Zbl 0243.47016)], M. Matos [Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations, IMECC-UNICAMP, State University of Campinas, São Paulo, Brasil (2007), http://www.ime.unicamp.br/rel_pesq/2007/rp03-07.html] and X. Mujica [Aplicações \(\tau (p;q)\)-somantes e \(\sigma (p)\)-nucleares, Thesis, State University of Campinas, São Paulo, Brasil (2006)].

MSC:

46G20 Infinite-dimensional holomorphy
46G25 (Spaces of) multilinear mappings, polynomials
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References:

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