Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
Copyright policy )Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for Π n=1 ∞ C and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) N-projective limits of Frechet spaces with a basis;2) countable direct sums of Frechet spaces with a basis;3) nuclear spaces.
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Banach analytic manifolds and spaces, Pseudoconvex domains, Topological linear spaces of continuous, differentiable or analytic functions
Other ``topological'' linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than \(\mathbb{R}\), etc.), Banach analytic manifolds and spaces, Pseudoconvex domains, Topological linear spaces of continuous, differentiable or analytic functions
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