Holomorphic Approximation and Hyperfunction Theory on a C1 Totally Real Submanifold of a Complex Manifold.
The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.
In questo articolo si determina il gruppo di tutti gli automorfismi olomorfi del dominio tubolare sul cono di Vinberg. Tale dominio ha dimensione complessa 5 ed è il dominio tubolare omogeneo non simmetrico di dimensione più bassa. Si costruisce esplicitamente un gruppo transitivo di automorfismi olomorfi del dominio; successivamente, dimostrando che tale gruppo contiene l'intero sottogruppo di isotropia di un qualunque punto, si ottiene che esso coincide col gruppo di tutti gli automorfismi olomorfi...
We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].
This work is an introduction to anisotropic spaces of holomorphic functions, which have -weight and are generalizations of Bloch spaces on a unit ball. We describe the holomorphic Bloch space in terms of the corresponding space. We establish a description of via the Bloch classes for all .