Remarques sur les suites d'unicité et l'analyticité partielle
Removable sets for holomorphic functions of several complex variables.
We show that every closed subset of CN that has finite (2N - 2)-dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ball.
Removable singularities and Liouville-type property of analytic multivalued functions
Removable singularities for Bloch and normal functions
Removable singularities for H... and for analytic functions with bounded Dirichlet integral.
Removable singularities for weighted Bergman spaces
We develop a theory of removable singularities for the weighted Bergman space , where is a Radon measure on . The set is weakly removable for if , and strongly removable for if . The general theory developed is in many ways similar to the theory of removable singularities for Hardy spaces, and locally Lipschitz spaces of analytic functions, including the existence of counterexamples to many plausible properties, e.g. the union of two compact removable singularities needs not be removable....
Removable Singularities of Analytic Functions of Severals Complex Variables.
Répartition des zéros et des pôles d'une fonction analytique
Report on Igusa's local zeta function
Representation of Distributions with Compact Support.
Representation of functions by logarithmic potential and reducibility of analytic functions of several variables.
The necessary and sufficient condition that a given plurisubharmonic or a subharmonic function admits the representation by the logarithmic potential (up to pluriharmonic or a harmonic term) is obtained in terms of the Radon transform. This representation is applied to the problem of representation of analytic functions by products of primary factors.
Representation theory for log-canonical surface singularities
We consider the representation theory for a class of log-canonical surface singularities in the sense of reflexive (or equivalently maximal Cohen-Macaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumeration of the indecomposable reflexive modules is given, and we prove that any reflexive module admits an integrable connection and hence is induced from a finite dimensional representation of the local fundamental...
Représentations linéaires des groupes kählériens et de leurs analogues projectifs
Dans cette note nous établissons le résultat suivant, annoncé dans [CCE13] : si est l’image d’une représentation linéaire d’un groupe kählérien , il admet un sous-groupe d’indice fini qui est l’image d’une représentation linéaire du groupe fondamental d’une variété projective complexe lisse .Il s’agit donc de la solution (à indice fini près) pour les représentations linéaires d’une question usuelle demandant si le groupe fondamental d’une variété kählérienne compacte est aussi celui d’une variété...
Représentations -adiques de dimension infinie de sous-groupes ouverts de
Representing measures for the disc algebra and for the ball algebra
We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.
Reproducing kernels and multiple interpolation by holomorphic functions
Reproducing kernels for holomorphic functions on some balls related to the Lie ball
We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.
Reproducing properties and -estimates for Bergman projections in Siegel domains of type II
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .
Réseaux de Kummer et surfaces K3.
Résidu de Grothendieck et forme de Chow.
We show an explicit relation between the Chow form and the Grothendieck residue; and we clarify the role that the residue can play in the intersection theory besides its role in the division problem.