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Dans cet article, nous étudions les zéros des fonctions holomorphes dans le bidisque dont le logarithme du module vérifie une condition de croissance : nous caractérisons par une condition de type Blaschke les zéros des fonctions vérifiant $\int_{D^{2}} δ_{\partial D^{2}} (z)^{α} {log}^{+} | f (z) | d λ (z) < \infty,$ pour $α > - 1$ , et nous donnons les conditions suffisantes pour des classes plus petites, en particulier pour la classe de Nevanlinna du bidisque.

Carathéodory balls and norm balls in $H_{p, n} = z \in ℂ^{n} : ∥ z ∥_{p} < 1$

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on $H_{p, n} = z \in ℂ^{n} : ∥ z ∥_{p} < 1$ which are balls with respect to the complex $l_{p}$ norm in $ℂ^{n}$ are those centered at the origin.

Carathéodory balls in convex complex ellipsoids

Włodzimierz Zwonek (1996)

Annales Polonici Mathematici

We consider the structure of Carathéodory balls in convex complex ellipsoids belonging to few domains for which explicit formulas for complex geodesics are known. We prove that in most cases the only Carathéodory balls which are simultaneously ellipsoids "similar" to the considered ellipsoid (even in some wider sense) are the ones with center at 0. Nevertheless, we get a surprising result that there are ellipsoids having Carathéodory balls with center not at 0 which are also ellipsoids.

Carleman Approximation on Totally Real Subsets of Class Ck.

Manne Per E. (1994)

Mathematica Scandinavica

Carleman's formulas and conditions of analytic extendability

L. Aizenberg (1995)

Banach Center Publications

Carleson measure in Bergman-Orlicz space of polydisc.

Xu, An-Jian, Yang, Zou (2010)

Abstract and Applied Analysis

Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji (2002)

Annales de l’institut Fourier

For a strongly pseudoconvex domain $D \subset ℂ^{n + 1}$ defined by a real polynomial of degree $k_{0}$ , we prove that the Lie group $Aut (D)$ can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$ , and that the sum of its Betti numbers is bounded by a certain constant $C_{n, k_{0}}$ depending only on $n$ and $k_{0}$ . In case $D$ is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...

Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of $C^{(} n + 1)$

Ryan, John (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Cauchy-Kowalewski theorems in Clifford analysis : a survey

Brackx, F., Delanghe, R., Sommen, F. (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Cauchy-Leray forms and vector bundles

Bo Berndtsson (1991)

Annales scientifiques de l'École Normale Supérieure

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Canvexité rationnelle des surfaces lagrangiennes.

Capacities associated to the Siciak extremal function

Capacity associated to a positive closed current. (Capacité associée à un courant positif fermé.)

Caractérisation de isomorphismes analytiques sur la boule-unité de Cn pour une norme.

Caractérisation des ellipsoïdes par leurs groupes d'automorphismes

Caractérisation tangentielle des classes de Carleman de fonctions holomorphes

Caractérisations des zéros des fonctions de certaines classes de type Nevanlinna dans le bidisque