On horospheres and holomorphic endomorfisms of the Siegel disc
On hulls of meromorphy and a class of Stein manifolds
On k-Pseudoflat Complex Spaces.
On matrix Reinhardt domains.
On meromorphic functions with values in locally convex spaces
On Non-Compact Complex Nil-Manifolds.
On nonimbeddability of Hartogs figures into complex manifolds
We prove the impossibility of imbeddings of Hartogs figures into general complex manifolds which are close to an imbedding of an analytic disc attached to a totally real collar. Analogously we provide examples of the so called thin Hartogs figures in complex manifolds having no neighborhood biholomorphic to an open set in a Stein manifold.
On non-Uniqueness of Complex Geodesies in Convex Bounded Domains
Si studiano «combinazioni convesse complesse» per mappe olomorfe dal disco unità di in un dominio convesso limitato di uno spazio di Banach complesso , e se ne traggono conseguenze sul carattere globale della non unicità per le geodetiche complesse di .
On Plurigenera of Normal Isolated Singularities. I.
On propagation of boundary continuity of holomorphic functions of several variables
We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail...
On proper R-actions on hyperbolic Stein surfaces.
On -Runge pairs
We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a -complete open subset (which is an analytic complement in the unit ball) such that the restriction map has a dense image for every but the pair is not a -Runge pair.
On Stein extensions of real symmetric spaces.
On Stein manifolds M for which 0 (M) is somorphic to ... as Fréchet spaces.
On the Automorphism Group of a Stein Manifold.
On the Bernstein-Walsh-Siciak theorem
By the Oka-Weil theorem, each holomorphic function f in a neighbourhood of a compact polynomially convex set can be approximated uniformly on K by complex polynomials. The famous Bernstein-Walsh-Siciak theorem specifies the Oka-Weil result: it states that the distance (in the supremum norm on K) of f to the space of complex polynomials of degree at most n tends to zero not slower than the sequence M(f)ρ(f)ⁿ for some M(f) > 0 and ρ(f) ∈ (0,1). The aim of this note is to deduce the uniform version,...
On the cohomology of twistor flag spaces
On the complex and convex geometry of Ol'shanskii semigroups
To a pair of a Lie group and an open elliptic convex cone in its Lie algebra one associates a complex semigroup which permits an action of by biholomorphic mappings. In the case where is a vector space is a complex reductive group. In this paper we show that such semigroups are always Stein manifolds, that a biinvariant domain is Stein is and only if it is of the form , with convex, that each holomorphic function on extends to the smallest biinvariant Stein domain containing ,...
On the CR-structure of certain linear group orbits in infinite dimensions
For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits explicitly and show as main result that every continuous CR-function on has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite...
On the -extension and the Hartogs extension