Special polyhedra for Reinhardt domains

Alexander Rashkovskii; Vyacheslav Zakharyuta

doi:10.1016/j.crma.2011.08.009

Complex Analysis

Special polyhedra for Reinhardt domains
[Polyèdres spéciaux pour des domaines de Reinhardt]

Présenté par : Jean-Pierre Demailly

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

Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 965-968.

Résumé
Abstract

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.

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.

Reçu le : 2010-10-28
Accepté le : 2011-08-16
Publié le : 2011-08-31

DOI : 10.1016/j.crma.2011.08.009

Affiliations des auteurs :

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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     title = {Special polyhedra for {Reinhardt} domains},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2011},
     doi = {10.1016/j.crma.2011.08.009},
     language = {en},
}

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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/

Bibliographie
Cité par

[1] A. Aytuna; A. Rashkovskii; V. Zahariuta Width asymptotics for a pair of Reinhardt domains, Ann. Polon. Math., Volume 78 (2002), pp. 31-38

[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 $C^{2}$ , 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 $C^{n}$ , 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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