Soit , un domaine à bord et un compact tel que soit connexe. On étudie l’extension holomorphe des fonctions CR définies sur à des sous-ensembles de . On dit que est CR-convexe si son enveloppe -convexe, , vérifie ( désigne l’espace des fonctions holomorphes sur et continues sur ). Le théorème principal de cet article prouve l’extension holomorphe à , si est CR-convexe.
Let , be a domain with -boundary and be a compact set such that is connected. We study univalent analytic extension of CR-functions from to parts of . Call CR-convex if its -convex hull, , satisfies ( denoting the space of functions, which are holomorphic on and continuous up to ). The main theorem of the paper gives analytic extension to , if is CR- convex.
Keywords: holomorphic hulls and holomorphic convexity, CR functions, removable singularities
Mot clés : enveloppes holomorphes et convexité holomorphe, CR fonctions, singularités éliminables
@article{AIF_2003__53_3_847_0, author = {Laurent-Thi\'ebaut, Christine and Porten, Egmon}, title = {Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity}, journal = {Annales de l'Institut Fourier}, pages = {847--857}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {3}, year = {2003}, doi = {10.5802/aif.1962}, mrnumber = {2008443}, zbl = {1035.32020}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1962/} }
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 SP - 847 EP - 857 VL - 53 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1962/ DO - 10.5802/aif.1962 LA - en ID - AIF_2003__53_3_847_0 ER -
%0 Journal Article %A Laurent-Thiébaut, Christine %A Porten, Egmon %T Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity %J Annales de l'Institut Fourier %D 2003 %P 847-857 %V 53 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1962/ %R 10.5802/aif.1962 %G en %F AIF_2003__53_3_847_0
Laurent-Thiébaut, Christine; Porten, Egmon. Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity. Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 847-857. doi : 10.5802/aif.1962. http://archive.numdam.org/articles/10.5802/aif.1962/
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