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We show that the projections of the pluripolar hull of the graph of an analytic function in a subdomain of the complex plane are open in the fine topology.
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Rocznik
Tom
Strony
285--290
Opis fizyczny
Bibliogr. 19 poz.
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autor
- Institute of Mathematics, Jagiellonian University Reymonta 4, 30-059 Krakow, Poland, Armen.Edigarian@im.uj.edu.pl
Bibliografia
- [Anc] A. Ancona, Démonstration d’une conjecture sur la capacité et l’effilement, C. R. Acad. Sci. Paris 297 (1983), 393-395.
- [Bre] M. Brelot, Eléments de la théorie classique du potentiel, Les cours de Sorbonne, Paris, 1958.
- [Edi] A. Edigarian, Pluripolar hulls and holomorphic coverings, Israel J. Math. 130 (2002), 77-92.
- [EdWi 1] A. Edigarian and J. Wiegerinck, The pluripolar hull of the graph of a holomorphic function with polar singularities, Indiana Univ. Math. J. 52 (2003), 1663-1680.
- [EdWi 2] —, —, Graphs that are not complete pluripolar, Proc. Amer. Math. Soc. 131 (2003), 2459-2465.
- [EdWi 3] —, —, Determination of the pluripolar hull of graphs of certain holomorphic functions, Ann. Inst. Fourier (Grenoble) 54 (2004), 2085-2104.
- [Edl] T. Edlund, Complete pluripolar curves and graphs, preprint, Dept. Math., Uppsala Univ., 2004.
- [E-J1] T. Edlund and B. Jöricke, The pluripolar hull of a graph and fine analytic continuation, arXiv:math.CV/0405025 (2004).
- [E-J2] T. Edlund and В. Jöricke, The pluripolar hull of a graph and fine analytic continuation, Ark. Mat., to appear.
- [Jos] B. Josefson, On the equivalence between locally polar and globally polar sets for plurisubharmonic functions on Cn, ibid. 16 (1978), 109-115.
- [LePo] N. Levenberg and E. A. Poletsky, Pluripolar hulls, Michigan Math. J. 46 (1999), 151-162.
- [LeMaPo] N. Levenberg, G. Martin and E. A. Poletsky, Analytic disks and pluripolar sets, Indiana Univ. Math. J. 41 (1992), 515-532.
- [Ran] Th. Ransford, Potential Theory in the Complex Plane, Cambridge Univ. Press, 1994.
- [Sad] A. Sadullaev, Plurisubharmonic measures and capacities on complex manifolds, Uspekhi Mat. Nauk 36 (1981), no. 4, 53-105 (in Russian).
- [Sic] J. Siciak, Pluripolar sets and pseudocontinuation, in: Complex Analysis and Dynamical Systems II (Nahariya, 2003), Amer. Math. Soc., Contemp. Math., to appear.
- [Wie 1] J. Wiegerinck, The pluripolar hull of {w = e-1/z}, Ark. Mat. 38 (2000), 201-208.
- [Wie 2] —, Graphs of holomorphic functions with isolated singularities are complete pluripolar, Michigan Math. J. 47 (2000), 191-197.
- [Zer] A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91.
- [Zwo] W. Zwonek, A note on pluripolar hulls of graphs of Blaschke products, Potential Anal. 22 (2005), 195-206.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0008-0028