Analytic extension from non-pseudoconvex boundaries and A(D)-convexity
Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 847-857.

Let D n ,n2, be a domain with C 2 -boundary and KD be a compact set such that DK is connected. We study univalent analytic extension of CR-functions from DK to parts of D. Call K CR-convex if its A(D)-convex hull, A(D)- hull (K), satisfies K=DA(D)- hull (K) (A(D) denoting the space of functions, which are holomorphic on D and continuous up to D). The main theorem of the paper gives analytic extension to DA(D)- hull (K), if K is CR- convex.

Soit D n ,n2, un domaine à bord C 2 et KD un compact tel que DK soit connexe. On étudie l’extension holomorphe des fonctions CR définies sur DK à des sous-ensembles de D. On dit que K est CR-convexe si son enveloppe A(D)-convexe, A(D)- hull (K), vérifie K=DA(D)- hull (K) (A(D) désigne l’espace des fonctions holomorphes sur D et continues sur D ¯). Le théorème principal de cet article prouve l’extension holomorphe à DA(D)- hull (K), si K est CR-convexe.

DOI: 10.5802/aif.1962
Classification: 32V25,  32D10,  32D20
Keywords: holomorphic hulls and holomorphic convexity, CR functions, removable singularities
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Laurent-Thiébaut, Christine; Porten, Egmon. Analytic extension from non-pseudoconvex boundaries and $$-convexity. Annales de l'Institut Fourier, Volume 53 (2003) no. 3, pp. 847-857. doi : 10.5802/aif.1962. https://aif.centre-mersenne.org/articles/10.5802/aif.1962/

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