Let B be the open unit ball for a norm on . Let f:B → B be a holomorphic map with f(0) = 0. We consider a condition implying that f is linear on . Moreover, in the case of the Euclidean ball , we show that f is a linear automorphism of under this condition.
We give a Schwarz lemma on complex ellipsoids.
In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.
We continue our previous work on a problem of Janiec connected with a uniqueness theorem, of Cartan-Gutzmer type, for holomorphic mappings in ℂⁿ. To solve this problem we apply properties of (j;k)-symmetrical functions.
Nous commençons par indiquer comment la connaissance du degré d’un opérateur différentiel, unitaire en et annulant , permet de donner un algorithme de calcul du polynôme de Bernstein d’un germe de fonction analytique à singularité isolée.Nous étudions alors le cas d’une singularité non dégénérée par rapport à son polygôme de Newton; nous donnons un algorithme pour calculer le polynôme de Bernstein de ces singularités et l’équation fonctionnelle associée. Notre méthode utilise une filtration...
Let be a pseudoconvex domain and let be a locally pluriregular set, j = 1,...,N. Put . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].
For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.