Geometry of nuclear spaces. II - Linear topological invariants
Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. I.
Gewichtete Räume stetiger vektorwertiger Funktionen und das injektive Tensorprodukt. II.
Holomorphic extension maps for spaces of Whitney jets.
The key result (Theorem 1) provides the existence of a holomorphic approximation map for some space of C∞-functions on an open subset of Rn. This leads to results about the existence of a continuous linear extension map from the space of the Whitney jets on a closed subset F of Rn into a space of holomorphic functions on an open subset D of Cn such that D ∩ Rn = RnF.
Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
Holomorphic Functions on (c0, Xb)-Modules.
Holomorphic functions on fully nuclear spaces
Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on
This article is devoted to a study of locally convex topologies on (where is an open subset of the locally convex topological vector space and is the set of all complex valued holomorphic functions on ). We discuss the following topologies on :(a) the compact open topology ,(b) the bornological topology associated with ,(c) the ported topology of Nachbin ,(d) the bornological topology associated with ; and(e) the topological of Nachbin.For balanced we show these topologies are...
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 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) -projective...
Imbedding of Power Series Spaces and Spaces of Analytic Functions.
Inductive limits and ...-tensor products.
Induktive Limites gewichteter Räume stetiger und holomorpher Funktionen.
Injektive Tensorprodukte und Slice-Produkte gewichteter Räume stetiger Funktionen.
Integral holomorphic functions
We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.
Integration in function spaces and differential equations with functional derivatives
Interpolating discrete multiplicity varieties for
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Interpolation de fonctions analytiques bornées
Interpolation d'opérateurs entre espaces de fonctions holomorphes
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...
Isometries of some F-algebras of holomorphic functions on the upper half plane
Linear isometries of N p(D) onto N p(D) are described, where N p(D), p > 1, is the set of all holomorphic functions f on the upper half plane D = {z ∈ ℂ: Im z > 0} such that supy>0 ∫ℝ lnp (1 + |(x + iy)|) dx < +∞. Our result is an improvement of the results by D.A. Efimov.
Isomorphism of spaces of bounded continuous functions