Integral representations on weakly pseudoconvex domains.
Intégrales singulières holomorphes
Invariant Forms on Complex Manifolds with Application to Holomorphic Mappings.
...k + a-estimates of the ...-equation on the Hartogs triangle.
Kernels of Martinelli-Bochner type on hypersurfaces.
-domains of holomorphy and the Bergman kernel
We give a characterization of -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.
L²-Angles between one-dimensional tubes
Le lemme fondamental de Nilsson dans le cas analytique local
On donne des évaluations précises de la croissance modérée des intégrales de fonctions de classe de Nilsson locale dans , exprimées par des caractéristiques topologiques des courbes de ramification des intégrands.
Le problème de l'inversion d'un théorème de Bremerman et ses applications à la transformation biholomorphe
Étude de la possibilité d’inverser le théorème de Bremerman : si et sont deux domaines bornés dans et et si , alors où désigne la fonction-noyau de Bergman. On introduit une classe de domaines dans qui contient les domaines de Reinhardt et de Hartogs et différentes fonctions “correctives” qui expriment la différence entre la fonction-noyau du domaine et le produit des fonctions-noyaux de sa “base” dans et de ses “fibres” dans . Divers moyens d’inverser le théorème de Bremerman...
Les noyaux de Bergman et Szegö pour des domaines strictment pseudo-convexes qui généralisent la boule.
Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions...
Lie group structures and reproducing kernels on the unit ball of
Si introducono due strutture di gruppo di Lie su un dominio di Siegel omogeneo di . Per la palla unitaria si definisce una famiglia ad un parametro di strutture intermedie; ad ognuna di esse viene associato naturalmente un nucleo riproducente ottenendo un'interpolazione tra il nucleo di Bergman ed il nucleo di Szego.
Line antiderivations over local fields and their applications.
Local regularity for the tangential Cauchy-Riemann complex.
Logarithmic Growth of the Bergman Kernel for Weakly Pseudoconvex Domains in ...3 of Finite Type.
Mesures de Monge-Ampère et mesures pluriharmoniques.
M-Harmonic Besov p-spaces and Hankel operators in the Bergman Space on the Ball in Cn.
Mittag-Leffler type expansions of -closed -forms in certain domains in
In this paper we will prove a Mittag-Leffler type theorem for -closed -forms in by addressing the question of constructing such differential forms with prescribed periods in certain domains.
Multidimensional residues and ideal membership.
Let I(f) be a zero-dimensional ideal in C[z1, ..., zn] defined by a mapping f. We compute the logarithmic residue of a polynomial g with respect to f. We adapt an idea introduced by Aizenberg to reduce the computation to a special case by means of a limiting process.We then consider the total sum of local residues of g w.r.t. f. If the zeroes of f are simple, this sum can be computed from a finite number of logarithmic residues. In the general case, you have to perturb the mapping f. Some applications...
Neuere Ergebnisse in der komplexen Analysis.
Non-holomorphic functional calculus for commuting operators with real spectrum
We consider -tuples of commuting operators on a Banach space with real spectra. The holomorphic functional calculus for is extended to algebras of ultra-differentiable functions on , depending on the growth of , , when . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.