Nous considérons un germe de feuilletage holomorphe singulier non-dicritique $ℱ$ défini sur une boule fermée $\overline{𝔹}\subset {ℂ}^2$, satisfaisant des hypothèses génériques, de courbe de séparatrice $S$. Nous démontrons l’existence d’un voisinage ouvert $U$ de $S$ dans $\overline{𝔹}$ tel que, pour toute feuille $L$ de ${ℱ}_{\left|\right(U\setminus S)}$, l’inclusion naturelle $ı:L\hookrightarrow U\setminus S$ induit un monomorphisme ${ı}_{*}:{\pi }_1\left(L\right)\hookrightarrow {\pi }_1(U\setminus S)$ au niveau du groupe fondamental. Pour cela, nous introduisons la notion géométrique de « connexité feuilletée » avec laquelle nous réinterprétons la notion d’incompressibilité....

We give a necessary condition for a holomorphic vector field to induce an integrable osculating plane distribution and, using this condition, we give a characterization of such fields. We also give a generic classification for vector fields which have two invariant coordinate planes.

In 1945 the first author introduced the classes $H^p\left(\alpha \right)$, 1 ≤ p<∞, α > -1, of holomorphic functions in the unit disk with finite integral (1) ∬ |f(ζ)|p (1-|ζ|²)α dξ dη < ∞ (ζ=ξ+iη) and established the following integral formula for $f\in H^p\left(\alpha \right)$: (2) f(z) = (α+1)/π ∬ f(ζ) ((1-|ζ|²)α)/((1-zζ̅)2+α) dξdη, z∈ . We have established that the analogues of the integral representation (2) hold for holomorphic functions in Ω from the classes $L^p(\Omega ;{\left[K\left(w\right)\right]}^{\alpha }dm\left(w\right))$, where: 1) $\Omega =w=(w₁,...,w_n)\in {ℂ}^n:Imw₁>{\sum }_{k=2}^n\left|w_k\right|²$, $K\left(w\right)=Imw₁-{\sum }_{k=2}^n\left|w_k\right|²$; 2) Ω is the matrix domain consisting of those complex m...

In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie groups and their algebraic subgroups. In particular, we show that in this setup invariant meromorphic functions separate orbits in general position. Applications to almost homogeneous spaces and principal orbit types are given. Furthermore, we use the main result...

Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone

The relationships between the JB*-triple structure of a complex spin factor S and the structure of the Hilbert space H associated to S are discussed. Every surjective linear isometry L of S can be uniquely represented in the form L(x) = mu.U(x) for some conjugation commuting unitary operator U on H and some mu belonging to C, |mu|=1. Automorphisms of S are characterized as those linear maps (continuity not assumed) that preserve minimal tripotents in S and the orthogonality relations among them.

Let $\mu$ be a measure on a domain $\Omega$ in ${ℂ}^n$ such that the Bergman space of holomorphic functions in $L^2(\Omega ,\mu )$ possesses a reproducing kernel $K(x,y)$ and $K(x,x)\&gt;0$$\forall x\in \Omega$. The Berezin transform associated to $\mu$ is the integral...