Remarks on the Bergman kernel function of a worm domain
We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be -smoothly extended to the boundary.
Remarks on the proof of a generalized Hartogs Lemma
This paper is an outgrowth of a paper by the first author on a generalized Hartogs Lemma. We complete the discussion of the nonlinear ∂̅ problem ∂f/∂z̅ = ψ(z,f(z)). We also simplify the proofs by a different choice of Banach spaces of functions.
Remarques sur les suites d'unicité et l'analyticité partielle
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....
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.
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 .
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.
Residue currents and complexity problems
Residue currents of the Bochner-Martinelli type.
Our objective is to construct residue currents from Bochner-Martinelli type kernels; the computations hold in the non complete intersection case and provide a new and more direct approach of the residue of Coleff-Herrera in the complete intersection case; computations involve crucial relations with toroidal varieties and multivariate integrals of the Mellin-Barnes type.
Residue currents with prescribed annihilator ideals
Residue integral formulas and the Radon transform for differential forms on q-linearly concave domains.
Residues, currents, and their relation to ideals of holomorphic functions.
Residues of regular and meromorphic differential forms.
Résidus et dualité.