EUDML

We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...

Convexity in complex analysis

Seán Dineen — 1995

Banach Center Publications

Holomorphy types on a Banach spaces

Seán Dineen — 1971

Studia Mathematica

Analytic functionals on fully nuclear spaces

Seán Dineen — 1982

Studia Mathematica

Surjective limits of locally convex spaces and their application to infinite dimensional holomorphy

Seán Dineen — 1975

Bulletin de la Société Mathématique de France

The Cartan-Thullen theorem for Banach spaces

Seán Dineen — 1970

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Holomorphic functions on Fréchet spaces with Schauder basis.

Seán Dineen — 1995

Extracta Mathematicae

Anticommutative analytic forms on fully nuclear spaces.

Séan Dineen — 1981

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen — 1973

Annales de l'institut Fourier

This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ : (a) the compact open topology $I_{0}$ , (b) the bornological topology associated with $I_{0}$ , (c) the ported topology of Nachbin $I_{ω}$ , (d) the bornological topology associated with $I_{ω}$ ; and (e) the $I_{ω}$ topological...

Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains

Sean Dineen — 1973

Annales de l'institut Fourier

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 $Π_{n = 1}^{\infty} C$ 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: ...