Approximation des fonctions analytiques avec croissance
Approximation d'operateurs d'extension minimale et de division.
Approximation of entire functions of two complex variables in Banach spaces.
Approximation of holomorphic functions of infinitely many variables II
Let be a Banach space and the ball of radius centered at . Can any holomorphic function on be approximated by entire functions, uniformly on smaller balls ? We answer this question in the affirmative for a large class of Banach spaces.
Approximation on the sphere by Besov analytic functions
Boundary values of zero-smooth Besov analytic functions in the unit ball of are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.
Approximation par des fonctions holomorphes à croissance contrôlée.
Let Ω be a bounded pseudo-convex domain in Cn with a C∞ boundary, and let S be the set of strictly pseudo-convex points of ∂Ω. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of S. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of Cn. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" in almost all normals arising...
Approximation polynômiale dans des classes de jets
In this paper we obtain results on approximation, in the multidimensional complex case, of functions from by complex polynomials. In particular, we generalize the results of Pawłucki and Pleśniak (1986) for the real case and of Siciak (1993) in the case of one complex variable. Furthermore, we extend the results of Baouendi and Goulaouic (1971) who obtained the order of approximation in the case of Gevrey classes over real compacts with smooth analytic boundary and we present the orders of approximation...
Approximation polynomiale et extension holomorphe avec croissance sur une variété algébrique
We first give a general growth version of the theorem of Bernstein-Walsh-Siciak concerning the rate of convergence of the best polynomial approximation of holomorphic functions on a polynomially convex compact subset of an affine algebraic manifold. This can be considered as a quantitative version of the well known approximation theorem of Oka-Weil. Then we give two applications of this theorem. The first one is a generalization to several variables of Winiarski's theorem relating the growth of...
Approximation pondérée de fonctions holomorphes dans un ouvert de
Approximation Theory on Totally Real Submanifolds.
Area differences under analytic maps and operators
Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping and that of , we study various norms for , where is the Toeplitz operator with symbol . In Theorem , given polynomials and we find a symbol such that . We extend some of our results to the polydisc.
Areas of Projections of Analytic Sets.
Arithmetische Eigenschaften ganzer Funktionen mehrerer Variablen.
Aspects of non-commutative function theory
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
Associated weights and spaces of holomorphic functions
When treating spaces of holomorphic functions with growth conditions, one is led to introduce associated weights. In our main theorem we characterize, in terms of the sequence of associated weights, several properties of weighted (LB)-spaces of holomorphic functions on an open subset which play an important role in the projective description problem. A number of relevant examples are provided, and a “new projective description problem” is posed. The proof of our main result can also serve to characterize...
Asymptotic behavior of the sectional curvature of the Bergman metric for annuli
We extend and simplify results of [Din 2010] where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly to [Din 2010] the description enables us to construct an infinitely connected planar domain (in our paper it is a Zalcman type domain) for which the supremum of the holomorphic sectional curvature is two, whereas its infimum is equal to -∞ .
Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in
Athe ...-Neumann Operator on the Unit Ball in Cn.
Automorphismes analytiques des produits continus de domaines bornés
Automorphismes analytiques d'un domaine de Reinhardt borné d'un espace de Banach à base
Dans cet article, j’étudie le groupe des automorphismes analytiques d’un domaine de Reinhardt borné d’un espace de Banach complexe à base. Je montre que, dans certains cas, ce groupe est un groupe de Lie banachique réel et je donne une classification complète des domaines de Reinhardt bornés homogènes. Pour certains espaces de Banach, je montre que les seuls automorphismes analytiques de la boule-unité ouverte sont linéaires.