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Displaying 41 – 60 of 346

Approximation par des fonctions holomorphes à croissance contrôlée.

Philippe Charpentier, Yves Dupain, Modi Mounkaila (1994)

Publicacions Matemàtiques

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 Theory on Totally Real Submanifolds.

Jeffrey Nunemacher (1976)

Mathematische Annalen

Asymptotic expansion of the Bergman kernel for weakly pseudoconvex tube domains in $𝐂^{2}$

Joe Kamimoto (1998)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Asymptotic Morse inequalities for pseudoconcave manifolds

George Marinescu (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...

Behaviour at the boundary of the complex Monge-Ampère equation

J. Lee, R. Melrose (1980/1981)

Séminaire Équations aux dérivées partielles (Polytechnique)

Bemerkungen zur Deformationstheorie nichtrationaler Singularitäten.

Oswald Riemenschneider (1974/1975)

Manuscripta mathematica

Biholomorphic invariants related to the Bergman functions [Book]

Maciej Skwarczyński (1980)

Boundary Behavior of Proper Holomorphic Correspondences.

S. Bell, E. Bedford (1985)

Mathematische Annalen

Boundary behaviour of holomorphic functions in Hardy-Sobolev spaces on convex domains in ℂⁿ

Marco M. Peloso, Hercule Valencourt (2010)

Colloquium Mathematicae

We study the boundary behaviour of holomorphic functions in the Hardy-Sobolev spaces $ℋ^{p, k} ()$ , where is a smooth, bounded convex domain of finite type in ℂⁿ, by describing the approach regions for such functions. In particular, we extend a phenomenon first discovered by Nagel-Rudin and Shapiro in the case of the unit disk, and later extended by Sueiro to the case of strongly pseudoconvex domains.

Boundary behaviour of invariant distances and complex geodesics

Marco Abate (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota viene studiato il comportamento al bordo delle distanze di Carathéodory e Kobayashi in domini fortemente pseudoconvessi di classe $\mathbf{C}^{2}$ . Come applicazione si dimostra che ogni geodetica complessa in tali domini è estendibile al bordo di classe $\mathbf{C}^{0,\frac{1}{2}}$ .

Boundary Regularity of Proper Holomorphic Mappings.

Klas Diederich, John E. Fornaess (1982)

Inventiones mathematicae

B-regularity of certain domains in ℂⁿ

Nguyen Quang Dieu, Nguyen Thac Dung, Dau Hoang Hung (2005)

Annales Polonici Mathematici

We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.

$C^{k}$ -estimates for the Cauchy-Riemann equations on certain weakly pseudoconvex domains

Jerzy Ryczaj (1987)

Colloquium Mathematicae

$C^{k}$ -estimates for the $\bar{\partial}$ -equation on concave domains of finite type

William Alexandre (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

$C^{k}$ estimates for convex domains of finite type in $ℂ^{n}$ are known from [7] for $k = 0$ and from [2] for $k > 0$ . We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching $z$ and $ζ$ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work. To overcome this problem...

Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang, Shanyu Ji (2002)

Annales de l’institut Fourier

For a strongly pseudoconvex domain $D \subset ℂ^{n + 1}$ defined by a real polynomial of degree $k_{0}$ , we prove that the Lie group $Aut (D)$ can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$ , and that the sum of its Betti numbers is bounded by a certain constant $C_{n, k_{0}}$ depending only on $n$ and $k_{0}$ . In case $D$ is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...

Currently displaying 41 – 60 of 346

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