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On the CR-structure of certain linear group orbits in infinite dimensions

Wilhelm Kaup — 2004

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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  M explicitly and show as main result that every continuous CR-function on  M has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes to infinite...

Hyperbolische komplexe Raüme

Wilhelm Kaup — 1968

Annales de l'institut Fourier

Dans la catégorie des espaces analytiques complexes on définit la notion d’esapce hyperbolique. Par exemple, Y est un espace hyperbolique, si Y admet un revêtement Y ˜ qui est séparé par les fonctions bornées holomorphes et qui jouit de la propriété suivante : (1) Y ˜ est homogène, ou (2) Y ˜ est revêtement d’un espace compact, ou (3) Y ˜ est un domaine borné strictement pseudoconvexe dans C n .

Bounded symmetric domains and derived geometric structures

Wilhelm Kaup — 2002

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Every homogeneous circular convex domain D C n (a bounded symmetric domain) gives rise to two interesting Lie groups: The semi-simple group G = A u t D of all biholomorphic automorphisms of D and its isotropy subgroup K G L n , C at the origin (a maximal compact subgroup of G ). The group G acts in a natural way on the compact dual X of D (a certain compactification of C n that generalizes the Riemann sphere in case D is the unit disk in C ). Various authors have studied the orbit structure of the G -space X , here we are interested...

On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces

Wilhelm KaupDmitri Zaitsev — 2006

Journal of the European Mathematical Society

We present a large class of homogeneous 2-nondegenerate CR-manifolds M , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains U , V in M extends to a global real-analytic CR-automorphism of M . We show that this class contains G -orbits in Hermitian symmetric spaces Z of compact type, where G is a real form of the complex Lie group Aut ( Z ) 0 and G has an open orbit that is a bounded symmetric domain of tube type.

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