Analytic extension from non-pseudoconvex boundaries and $A\left(D\right)$-convexity

Laurent-Thiébaut, Christine, and Porten, Egmon. "Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity." Annales de l’institut Fourier 53.3 (2003): 847-857. <http://eudml.org/doc/116055>.

@article{Laurent2003,
abstract = {Let $D\subset \subset \{\mathbb \{C\}\}^n,n\ge 2$, be a domain with $C^2$-boundary and $K\subset \partial D$ be a compact set such that $\partial D\backslash K$ is connected. We study univalent analytic extension of CR-functions from $\partial D\backslash K$ to parts of $D$. Call $K$ CR-convex if its $A(D)$-convex hull, $A(D)-\{\rm hull\}(K)$, satisfies $K=\partial D\cap A(D)-\{\rm hull\}(K)$ ($A(D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$). The main theorem of the paper gives analytic extension to $\partial D\backslash A(D)-\{\rm hull\}(K)$, if $K$ is CR- convex.},
affiliation = {Université Joseph Fourier, Institut Fourier, BP 74, 3802 Saint-Martin d'Hères Cedex (France); Humboldt-University, Mathematics Department, Rudower Chaussee 25, 12489 Berlin (Allemagne)},
author = {Laurent-Thiébaut, Christine, Porten, Egmon},
journal = {Annales de l’institut Fourier},
keywords = {holomorphic hulls and holomorphic convexity; CR functions; removable singularities; holomorphic hulls; holomorphic convexity; analytic extension; CR-convex},
language = {eng},
number = {3},
pages = {847-857},
publisher = {Association des Annales de l'Institut Fourier},
title = {Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity},
url = {http://eudml.org/doc/116055},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Laurent-Thiébaut, Christine
AU - Porten, Egmon
TI - Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 3
SP - 847
EP - 857
AB - Let $D\subset \subset {\mathbb {C}}^n,n\ge 2$, be a domain with $C^2$-boundary and $K\subset \partial D$ be a compact set such that $\partial D\backslash K$ is connected. We study univalent analytic extension of CR-functions from $\partial D\backslash K$ to parts of $D$. Call $K$ CR-convex if its $A(D)$-convex hull, $A(D)-{\rm hull}(K)$, satisfies $K=\partial D\cap A(D)-{\rm hull}(K)$ ($A(D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$). The main theorem of the paper gives analytic extension to $\partial D\backslash A(D)-{\rm hull}(K)$, if $K$ is CR- convex.
LA - eng
KW - holomorphic hulls and holomorphic convexity; CR functions; removable singularities; holomorphic hulls; holomorphic convexity; analytic extension; CR-convex
UR - http://eudml.org/doc/116055
ER -