Holomorphy types and the Fourier-Borel transform between spaces of entire functions of a given type and order defined on Banach spaces
Let E be a Banach space and Θ be a π_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 Exp _Θ,A^k(E) of entire functions on E of order k and Θ-type strictly less than A and the space Exp _Θ^′,0,(λ (k) A)^-1 ^k^′ (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 Exp _Θ,A^k(E) of entire functions on E of order k and Θ-type less than or equal to A and the space Exp _Θ^′, (λ(k)A)^-1 ^k^′ ( 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., number=1, journal=MATHEMATICA SCANDINAVICA, author=Fávaro, Vinícius V. and Jatobá, Ariosvaldo M., year=2012, month=Mar., pages=111–139