@article{Fávaro_Jatobá_2012, title={Holomorphy types and the Fourier-Borel transform between spaces of entire functions of a given type and order defined on Banach spaces}, volume={110}, url={https://www.mscand.dk/article/view/15200}, DOI={10.7146/math.scand.a-15200}, abstractNote={Let $E$ be a Banach space and $\Theta$ be a $\pi_{1}$-holomorphy type. The main purpose of this paper is to show that the Fourier-Borel transform is an algebraic isomorphism between the dual of the space ${\operatorname{Exp }_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type strictly less than $A$ and the space ${\operatorname{Exp }_{\Theta^{\prime},0,(\lambda (k) A)^{-1 }^{k^{\prime }(E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type less than or equal to $(\lambda(k)A)^{-1}$. The same is proved for the dual of the space ${\operatorname{Exp }_{\Theta,A}^{k}(E)$ of entire functions on $E$ of order $k$ and $\Theta$-type less than or equal to $A$ and the space ${\operatorname{Exp }_{\Theta^{\prime}, (\lambda(k)A)^{-1 }^{k^{\prime }( E^{\prime})$ of entire functions on $E^{\prime}$ of order $k^{\prime}$ and $\Theta^{\prime}$-type strictly less than $(\lambda(k)A)^{-1}$. Moreover, the Fourier-Borel transform is proved to be a topological isomorphism in certain cases.}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Fávaro, Vinícius V. and Jatobá, Ariosvaldo M.}, year={2012}, month={Mar.}, pages={111–139} }