Holomorphic functions on Fréchet spaces with Schauder basis.
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...
Holomorphic functions on strict inductive limits of Banach spaces.
In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
Holomorphic germs on Banach spaces
Let and be two complex Banach spaces, a nonempty subset of and a compact subset of . The concept of holomorphy type between and , and the natural locally convex topology on the vector space of all holomorphic mappings of a given holomorphy type from to were considered first by L. Nachbin. Motived by his work, we introduce the locally convex space of all germs of holomorphic mappings into around of a given holomorphy type , and study its interplay with and some...
Holomorphic isometries of Cartan domains of type four
The holomorphic isometries for the Kobayashi metric of Cartan domains of type four are characterized.
Holomorphic isometries of Cartan domains of type one
Holomorphic isometries for the Kobayashi metric of a class of Cartan domains are characterized.
Holomorphic mappings of uniformly bounded type and the linear topological invariants , and .
Holomorphic maps of uniform type
Holomorphic retractions and boundary Berezin transforms
In an earlier paper, the first two authors have shown that the convolution of a function continuous on the closure of a Cartan domain and a -invariant finite measure on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face depends only on the restriction of to and is equal to the convolution, in , of the latter restriction with some measure on uniquely determined by . In this article, we give an explicit formula for in terms of ,...
Holomorphic semigroups in interpolation and extrapolation spaces.
Holomorphic semigroups of holomorphic isometries
A previous paper was devoted to the construction of non-trivial holomorphic families of holomorphic isometries for the Carathéodory metric of a bounded domain in a complex Banach space, fixing a point in the domain. The present article shows that such a family cannot exist if it contains a strongly continuous one parameter semigroup.
Holomorphic Sobolev spaces on the ball [Book]
Holomorphically Closed Algebras of Analytic Functions.
Holomorphically Dependent Generalised Inverses.
Holomorphy types and ideals of multilinear mappings
We explore a condition under which the ideal of polynomials generated by an ideal of multilinear mappings between Banach spaces is a global holomorphy type. After some examples and applications, this condition is studied in its own right. A final section provides applications to the ideals formed by multilinear mappings and polynomials which are absolutely (p;q)-summing at every point.
Holomorphy types and spaces of entire functions of bounded type on Banach spaces
In this paper spaces of entire functions of -holomorphy type of bounded type are introduced and results involving these spaces are proved. In particular, we “construct an algorithm” to obtain a duality result via the Borel transform and to prove existence and approximation results for convolution equations. The results we prove generalize previous results of this type due to B. Malgrange: Existence et approximation des équations aux dérivées partielles et des équations des convolutions. Annales...
Holomorphy types for open subsets of a Banach space
Homeomorphic measures on products of intervals.