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We show that a CR function of class $C^{k}$ , 0 ≤ k < ∞, on a tube submanifold of $ℂ^{n}$ 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 $C^{k}$ -norm of the extension is shown to be no bigger than the $C^{k}$ -norm of the original CR function.

The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition

Martin Schottenloher (1976)

Annales de l'institut Fourier

It is proved that the Levi problem for certain locally convex Hausdorff spaces $E$ over $C$ 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 $E$ 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.

T. Dietmair (1993)

Mathematische Annalen

The Oka-Weil theorem in locally convex spaces with the approximation property

Jorge Mujica (1977/1978)

Séminaire Paul Krée

The Oka-Weil theorem in topological vector spaces

Bui Dac Tac (1991)

Annales Polonici Mathematici

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 $ℂ^{n}$

Ulf Backlund, Anders Fällström (1996)

Colloquium Mathematicae

We prove that three pairwise disjoint, convex sets can be found, all congruent to a set of the form $(z_{1}, z_{2}, z_{3}) \in ℂ^{3} : | z_{1} |^{2} + | z_{2} |^{2} + {| z_{3} |}^{2 m} \leq 1$ , 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.

W. Kucharz (1995)

Mathematische Zeitschrift

The use of D-modules to study exponential polynomials

C. Berenstein, A. Yger (1995)

Banach Center Publications

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.

J. Duval (1988)

Mathematische Annalen

Une formule d'interpolation en deux variables

Damien Roy (2001)

Journal de théorie des nombres de Bordeaux

On démontre une formule d’interpolation pour une fonction $F (z, w)$ de deux variables complexes qui tient compte des valeurs de cette fonction ainsi que de ses dérivées partielles par rapport à $w$ en des points d’un sous-groupe de $𝐂^{2}$ de rang $2$ . 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.

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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 $C^{k}$ CR functions on tube submanifolds

The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition

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

The polynomial hull of unions of convex sets in $ℂ^{n}$

The Runge approximation problem for holomorphic maps into Grassmannians.

The use of D-modules to study exponential polynomials

Une exemple de disque polynomialement convexe.

Une formule d'interpolation en deux variables

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

Currently displaying 101 – 120 of 132