Resumen de Homolomorphy types and the Fourier-Borel transform between spaces of entire functions of a given type and order defined on Banach spaces

Vinícius V. Fávaro, Ariosvaldo M. Jatobá

• Let E be a Banach space and Θ be a π1-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 ExpkΘ,A(E) of entire functions on E of order k and Θ-type strictly less than A and the space Expk′Θ′,0,(λ(k)A)−1(E′) of entire functions on E′ of order k′ and Θ′-type less than or equal to (λ(k)A)−1. The same is proved for the dual of the space ExpkΘ,A(E) of entire functions on E of order k and Θ-type less than or equal to A and the space Expk′Θ′,(λ(k)A)−1(E′) of entire functions on E′ of order k′ and Θ′-type strictly less than (λ(k)A)−1. Moreover, the Fourier-Borel transform is proved to be a topological isomorphism in certain cases.