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Internal characteristics of domains in ℂⁿ

Vyacheslav Zakharyuta (2014)

Annales Polonici Mathematici

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 sequences, Carleson measures and Wirtinger inequality

Eric Amar (2008)

Annales Polonici Mathematici

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 μ S : = a S ( 1 - | a | ² ) δ a 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 μ S 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...

Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere (1991)

Annales Polonici Mathematici

Let K be a compact subset of an hyperconvex open set D n , 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 H ( D α ) is a continuous...

Interpolation sur des perturbations d’ensembles produits

Damien Roy (2002)

Bulletin de la Société Mathématique de France

On démontre un résultat concernant l’interpolation de fonctions analytiques sur une perturbation d’ensemble produit qui, dans le cas p -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.

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