...k + a-estimates of the ...-equation on the Hartogs triangle.
k-holomorphe Vektorraumbündel auf offenen Polyzylindern.
Le problème de l'inversion d'un théorème de Bremerman et ses applications à la transformation biholomorphe
Étude de la possibilité d’inverser le théorème de Bremerman : si et sont deux domaines bornés dans et et si , alors où désigne la fonction-noyau de Bergman. On introduit une classe de domaines dans qui contient les domaines de Reinhardt et de Hartogs et différentes fonctions “correctives” qui expriment la différence entre la fonction-noyau du domaine et le produit des fonctions-noyaux de sa “base” dans et de ses “fibres” dans . Divers moyens d’inverser le théorème de Bremerman...
L'équation de la chaleur en plusieurs variables complexes
Les équations de Hua d'un domaine borné symétrique du type tube.
Levi curvature with radial symmetry : a sphere theorem for bounded Reinhardt domains of
Maps from the Two-Ball to the Three-Ball.
Moduli for pointed convex domains.
Multidimensional analogue of the van der Corput-Visser inequality and its application to the estimation of the Bohr radius
We present a multidimensional analogue of an inequality by van der Corput-Visser concerning the coefficients of a real trigonometric polynomial. As an application, we obtain an improved estimate from below of the Bohr radius for the hypercone 𝓓₁ⁿ = {z ∈ ℂⁿ: |z₁|+. .. +|zₙ| < 1} when 3 ≤ n ≤ 10.
Negligible sets and good functions on polydiscs
A notion of negligible sets for polydiscs is introduced. Some properties of non-negligible sets are proved. These results are used to construct good and good inner functions on polydiscs.
Non-extendable holomorphic functions
Non-extendable holomorphic functions of bounded growth in Reinhardt domains
Normed domains of holomorphy.
Note on integral representation of holomorphic functions in several complex variables
On a Domain Equivalent to the Bidisk.
On a Minimal Complex Norm that Extends the Real Euclidean Norm.
On a minimum principle in several complex variables
On a space of smooth functions on a convex unbounded set in ℝn admitting holomorphic extension in ℂn
For some given logarithmically convex sequence M of positive numbers we construct a subspace of the space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in ℝn. Due to the conditions on M each function of this space admits a holomorphic extension in ℂn. In the current article, the space of holomorphic extensions is considered and Paley-Wiener type theorems are established. To prove these theorems, some auxiliary results on extensions of holomorphic functions...
On approximation by special analytic polyhedral pairs
For bounded logarithmically convex Reinhardt pairs "compact set - domain" (K,D) we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping f: D → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(D,K;z) by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary...
On Bergman completeness of pseudoconvex Reinhardt domains