Schlichte Linearkombinationen holomorpher Funktionen aus H (D).
Séries de Laurent des fonctions holomorphes dans la complexification d'un espace symétrique compact
Siciak's extremal function in complex and real analysis
The Siciak extremal function establishes an important link between polynomial approximation in several variables and pluripotential theory. This yields its numerous applications in complex and real analysis. Some of them can be found on a rich list drawn up by Klimek in his well-known monograph "Pluripotential Theory". The purpose of this paper is to supplement it by applications in constructive function theory.
Siciak-Zahariuta extremal functions and polynomial hulls
We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.
Some applications of functions of several complex variables to Toeplitz and subnormal operators
Some Characterizations of L-regular Points.
Some open problems in higher dimensional complex analysis and complex dynamics.
We present a collection of problems in complex analysis and complex dynamics in several variables.
Some Properties of Compact Natural Sets in Several Complex Variables.
Some capacities and applications - the lemma on mixed derivatives revisited
Some remarks concerning holomorphically convex hulls and envelopes of holomorphy.
Some results on the extension of analytic entities defined out of a compact
Special neighborhoods of subsets in complex spaces.
Spherical Stein manifolds and the Weyl involution
We consider an action of a connected compact Lie group on a Stein manifold by holomorphic transformations. We prove that the manifold is spherical if and only if there exists an antiholomorphic involution preserving each orbit. Moreover, for a spherical Stein manifold, we construct an antiholomorphic involution, which is equivariant with respect to the Weyl involution of the acting group, and show that this involution stabilizes each orbit. The construction uses some properties of spherical subgroups...
Stability of the polynomial hull of
Stein manifolds with compact symmetric center.
Stein Neighborhoods for Finite Preimages of Regular Domain.
Stein open subsets with analytic complements in compact complex spaces
Let Y be an open subset of a reduced compact complex space X such that X - Y is the support of an effective divisor D. If X is a surface and D is an effective Weil divisor, we give sufficient conditions so that Y is Stein. If X is of pure dimension d ≥ 1 and X - Y is the support of an effective Cartier divisor D, we show that Y is Stein if Y contains no compact curves, for all i > 0, and for every point x₀ ∈ X-Y there is an n ∈ ℕ such that is empty or has dimension 0, where is the map from...
Stein Quotients of Connected Complex Lie Groups.
Stein surfaces associated to intermediate Kato surfaces. (Surfaces de Stein associées aux surfaces de Kato intermédiaires.)
Steinness of bundles with fiber a Reinhardt bounded domain
Let denote a holomorphic bundle with fiber and with basis . Both and are assumed to be Stein. For a Reinhardt bounded domain of dimension or , we give a necessary and sufficient condition on for the existence of a non-Stein such (Theorem ); for , we give necessary and sufficient criteria for to be Stein (Theorem ). For a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for to be Stein (Theorem ).