Algebraic projective descriptions and the Fantappiè transformation

Abstract

Let H(Q) be the space of all the functions which are holomorphic on an open neighbourhood of a convex locally closed subset Q of $$\mathbb C^N$$ , endowed with its natural projective topology. We characterize when the countable weighted inductive limit of Frechet spaces which is obtained as the Fourier Laplace transform of the dual $$H(Q)'$$ of H(Q) coincides algebraically with its projective hull.