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
On the disc-convexity of complex Banach manifolds
The Banach hyperbolicity and disc-convexity of complex Banach manifolds and their relations are investigated.
On the embedding of 1-convex manifolds with 1-dimensional exceptional sets.
On the existence of bounded holomorphic functions on complete Kähler manifolds.
On the extension of L2 holomorphic functions III: negligible weights.
On the homology groups of -complete spaces
On the homology groups of Stein spaces and Runge pairs.
On the invertibility of isometric semigroup representations
Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum . For or , we establish connections with polynomial convexity.
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the Polynomial Convexity of the Union ot Two Maximal Totally Real Subspaces of Cn.
On the spectra of holomorphic function algebras
On the spectral sequence fo r the -cohomology of a holomorpkic bundle with Stein fibres
Si esamina la successione spettrale per la -coomologia dello spazio totale di un fibrato olomorfo nel caso in cui le fibre siano varietà di Stein.
On the Thickness of the Shilov Boundary.