Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.
Holomorphic approximation in infinite-dimensional Riemann domains
-domains of holomorphy and the Bergman kernel
We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.
La réciproque du théorème d'annulation et de finitude de cohomologie dans l'espace produit d'une famille dénombrable de sphères de Riemann
Le problème de Lévi dans certains espaces vectoriels topologiques localement convexes
Le problème de Levi en dimension infinie
Non-extendable holomorphic functions
Non-extendable holomorphic functions of bounded growth in Reinhardt domains
Non-subharmonicity of the Hausdorff distance
Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.
Normed domains of holomorphy.
On 2-Dimensional Cousin I-Spaces.
On balanced L²-domains of holomorphy
We show that any bounded balanced domain of holomorphy is an -domain of holomorphy.
On invariant domains of holomorphy
On n-circled -domains of holomorphy
We present various characterizations of n-circled domains of holomorphy with respect to some subspaces of .
On the complex and convex geometry of Ol'shanskii semigroups
To a pair of a Lie group and an open elliptic convex cone in its Lie algebra one associates a complex semigroup which permits an action of by biholomorphic mappings. In the case where is a vector space is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain is Stein is and only if it is of the form , with convex, that each holomorphic function on extends to the smallest biinvariant Stein domain containing ,...
On the complex geometry of invariant domains in complexified symmetric spaces
Let be a real symmetric space and the corresponding decomposition of the Lie algebra. To each open -invariant domain consisting of real ad-diagonalizable elements, we associate a complex manifold which is a curved analog of a tube domain with base , and we have a natural action of by holomorphic mappings. We show that is a Stein manifold if and only if is convex, that the envelope of holomorphy is schlicht and that -invariant plurisubharmonic functions correspond to convex -invariant...
On the extended tube conjecture.
Prolongement analytique en dimension infinie
On construit l’enveloppe d’holomorphie d’un domaine étalé au-dessus d’un espace de Banach. Cette enveloppe ne dépend pas de l’étalement et possède la propriété du disque ; certains théorèmes de Cartan-Thullen se généralisent. Les applications analytiques de dans un e.l.c. se prolongent à lorsque est un espace de Banach et dans certains autres cas. Enfin, les espaces de fonctions analytiques sur et sur ont les mêmes bornés.
Prolongement des fonctions holomorphes bornèes et métrique de Carathéodory.
Pseudoconvex Domains: An Example with Nontrivial Nebenhülle.