Comptes Rendus
Complex Analysis
Special polyhedra for Reinhardt domains
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 965-968.

We show that every bounded hyperconvex Reinhardt domain can be approximated by special polynomial polyhedra defined by homogeneous polynomial mappings. This is achieved by means of approximation of the pluricomplex Green function of the domain with pole at the origin.

Nous montrons que tout domaine de Reinhardt borné et hyperconvexe est approché extérieurement par des polyèdres polynomiaux spéciaux définis par des applications polynomiales homogènes. Ceci se fait à lʼaide dʼune certaine approximation de la fonction de Green pluricomplexe du domaine avec pôle à lʼorigine.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2011.08.009
Alexander Rashkovskii 1; Vyacheslav Zakharyuta 2

1 Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway
2 Sabanci University, 34956 Tuzla, Istanbul, Turkey
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Alexander Rashkovskii; Vyacheslav Zakharyuta. Special polyhedra for Reinhardt domains. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 965-968. doi : 10.1016/j.crma.2011.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.009/

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[2] A. Aytuna; V. Zakharyuta On Lelong–Bremermann lemma, Proc. AMS, Volume 136 (2008) no. 5, pp. 1733-1742

[3] T. Bloom; N. Levenberg; Yu. Lyubarskii A Hilbert lemniscate theorem in C2, Ann. Inst. Fourier (Grenoble), Volume 58 (2008) no. 6, pp. 2191-2220

[4] S. Nivoche Convexité polynomiale, polyhèdres polynomiaux spéciaux et applications, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006) no. 11, pp. 825-830

[5] S. Nivoche Polynomial convexity, special polynomial polyhedra and the pluricomplex Green function for a compact set in Cn, J. Math. Pures Appl., Volume 91 (2009), pp. 364-383

[6] T. Ransford Potential Theory in the Complex Plane, Cambridge University Press, 1995

[7] V.P. Zahariuta, Spaces of analytic functions and maximal plurisubharmonic functions, D.Sci. Dissertation, Rostov-on-Don, 1984.

[8] V. Zahariuta, Spaces of analytic functions and complex potential theory, in: Linear Topological Spaces and Complex Analysis, vol. 1, 1994, pp. 74–146.

[9] V. Zahariuta On approximation by special analytic polyhedral pairs, Ann. Polon. Math., Volume 80 (2003), pp. 243-256

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