Displaying 21 – 40 of 406

Showing per page

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

Philippe Charpentier (1984)

Annales de l'institut Fourier

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 D 2 δ D 2 ( z ) α log + | f ( z ) | d λ ( z ) < , 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 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 n : z p < 1 which are balls with respect to the complex l p norm in 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.

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 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 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...

Currently displaying 21 – 40 of 406