Inner Functions and Boundary Values in H... (...) and A (...) in Smoothly Bounded Pseudoconvex Domains.
Internal characteristics of domains in ℂⁿ
This paper is devoted to internal capacity characteristics of a domain D ⊂ ℂⁿ, relative to a point a ∈ D, which have their origin in the notion of the conformal radius of a simply connected plane domain relative to a point. Our main goal is to study the internal Chebyshev constants and transfinite diameters for a domain D ⊂ ℂⁿ and its boundary ∂D relative to a point a ∈ D in the spirit of the author's article [Math. USSR-Sb. 25 (1975), 350-364], where similar characteristics have been investigated...
Interpolating discrete multiplicity varieties for
A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space .
Interpolating sequences, Carleson measures and Wirtinger inequality
Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual bounded sequence...
Interpolating sequences of complex hyperplanes in the unit ball of
A sufficient condition is given to make a sequence of hyperplanes in the complex unit ball an interpolating sequence for , i.e. bounded holomorphic functions on the hyperplanes can be boundedly extended.
Interpolation d'opérateurs entre espaces de fonctions holomorphes
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...
Interpolation in Weakly Pseudoconvex Domains in C2.
Interpolation manifolds
Interpolation sur des perturbations d’ensembles produits
On démontre un résultat concernant l’interpolation de fonctions analytiques sur une perturbation d’ensemble produit qui, dans le cas -adique, répond à une conjecture de P.Robba et, dans le cas complexe, complète des résultats antérieurs de E.Bombieri, S.Lang, D.Masser, J.-C.Moreau et M.Waldschmidt.
Intervention de la bornologie dans la convexité holomorphe