Sur la caractérisation des automorphismes analytiques d'un domaine borné
Sur un problème de W. Rudin concernant les fonctions holomorphes et borneés
Survey of Oka theory.
The generalized three circle- and other convexity theorems with application to the construction of envelopes of holomorphy
The holomorphic extension of CR functions on tube submanifolds
We show that a CR function of class , 0 ≤ k < ∞, on a tube submanifold of holomorphically extends to the convex hull of the submanifold. The extension and all its derivatives through order k are shown to have nontangential pointwise boundary values on the original tube submanifold. The -norm of the extension is shown to be no bigger than the -norm of the original CR function.
The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition
It is proved that the Levi problem for certain locally convex Hausdorff spaces over with a finite dimensional Schauder decomposition (for example for Fréchet or Silva spaces with a Schauder basis) the Levi problem has a solution, i.e. every pseudoconvex domain spread over is a domain of existence of an analytic function. It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies...
The Mergelyan-Bishop theorem in the case of mapping into homogeneous manifolds. II. Proof of the theorem and application.
The Oka-Weil theorem in locally convex spaces with the approximation property
The Oka-Weil theorem in topological vector spaces
It is shown that a sequentially complete topological vector space X with a compact Schauder basis has WSPAP (see Definition 2) if and only if X has a pseudo-homogeneous norm bounded on every compact subset of X.
The polynomial hull of unions of convex sets in
We prove that three pairwise disjoint, convex sets can be found, all congruent to a set of the form , such that their union has a non-trivial polynomial convex hull. This shows that not all holomorphic functions on the interior of the union can be approximated by polynomials in the open-closed topology.
The Runge approximation problem for holomorphic maps into Grassmannians.
The use of D-modules to study exponential polynomials
This is a summary of recent work where we introduced a class of D-modules adapted to study ideals generated by exponential polynomials.
Une exemple de disque polynomialement convexe.
Une formule d'interpolation en deux variables
On démontre une formule d’interpolation pour une fonction de deux variables complexes qui tient compte des valeurs de cette fonction ainsi que de ses dérivées partielles par rapport à en des points d’un sous-groupe de de rang . On explique préalablement comment, dans les grandes lignes, une telle formule permet de ramener la conjecture de Schanuel à un énoncé dont la forme est celle d’un critère d’indépendance algébrique.
Uniform approximation by polynomials on real non-degenerate Weil polyhedron.
Uniform Approximation of Holomorphic Functions on Bounded Hartogs Domains in C2.
Uniform Approximation on Totally Real Sets.
Valeurs au bord de fonctions holomorphes bornées en plusieurs variables complexes
Variation of the Green function of Riemann surfaces and Whitney's holomorphic stratification conjecture
Weierstrassova věta o aproximaci