In this article we study the Fourier–Borel transform between the dual of ExpkÑ,(s;( r,q)),A(E), the space of entire functions on E of (s;(r,q))-quasi-nuclear order k and (s;(r,q))-quasi-nuclear type strictly less than A, and the space Expk'(s',m(r';q')),0,(θ(k)A)−1(E') of entire functions on E' of (s',m(r';q'))-summing order k and (s',m(r';q'))-summing type less than or equal to (θ(k)A)−1. This mapping identifies algebraically and topologically these two spaces. On the dual space it is considered the strong topology. This generalizes results of Matos  and Martineau .
Cite this article
Vinícius Vieira Fávaro, The Fourier–Borel transform between spaces of entire functions of a given type and order. Port. Math. 65 (2008), no. 2, pp. 285–309DOI 10.4171/PM/1813