Some boundary-value properties of an analytic function in a bicylinder
Some properties of Reinhardt domains
We first establish the equivalence between hyperconvexity of a fat bounded Reinhardt domain and the existence of a Stein neighbourhood basis of its closure. Next, we give a necessary and sufficient condition on a bounded Reinhardt domain D so that every holomorphic mapping from the punctured disk into D can be extended holomorphically to a map from Δ into D.
Spatial Riemann problem for analytic functions of two complex variables.
Stability of Envelopes of Holomorphy and the Degenerate Monge-Ampère Equation.
Stability of the Monge-Ampère Foliation.
Stability of the polynomial hull of
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 ).
Strange complex structures on Euclidean space.
Strong boundedness of analytic functions in tubes.
Sur la transformation de Fourier-Laurent dans un groupe analytique complexe réductif
Soit un groupe analytique compact : son complexifié universel est un groupe analytique complexe réductif. On introduit dans une classe de “domaines de Reinhardt généralisés”, bi-invariants par et caractérisés par une “base”, définie dans une sous-algèbre abélienne maximale de l’algèbre de Lie du groupe et invariante par le groupe de Weyl.On donne une caractérisation par leurs coefficients de Fourier-Laurent des fonctions holomorphes dans un tel domaine. On montre que l’enveloppe d’holomorphie...
Sur la valeur au bord du noyau de Poisson d'un domaine borné symétrique.
Sur une caractérisation de la boule parmi les domaines de par son groupe d’automorphismes
Nous prouvons en particulier que tout domaine homogène borné de , à frontière deux fois continûment différentiable est bi-holomorphiquement équivalent à la boule unité de . Les démonstrations sont entièrement élémentaires.
Temlyakovsche Integraldarstellungen.
The Bloch space for the minimal ball
We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.
The exceptional sets for functions from the Bergman space
The extended future tube conjecture for SO(1, )
Let be the open upper light cone in with respect to the Lorentz product. The connected linear Lorentz group acts on and therefore diagonally on the -fold product where We prove that the extended future tube is a domain of holomorphy.
The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains
We consider a certain class of unbounded nonhyperbolic Reinhardt domains which is called the twisted Fock-Bargmann-Hartogs domains. By showing Cartan's linearity theorem for our unbounded nonhyperbolic domains, we give a complete description of the automorphism groups of twisted Fock-Bargmann-Hartogs domains.
The Iversen theorem in a polydisc.
The micro-support of the complex defined by a convolution operator in tube domains
The Serre problem with Reinhardt fibers
The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.