Arkiv för Matematik

, Volume 43, Issue 1, pp 181–200 | Cite as

Continuity of pluricomplex Green functions with poles along a hypersurface

  • Quang Dieu Nguyen


Green Function Pluricomplex Green Function 


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  1. [AW]Alexander, H. andWermer, J.,Several Complex Variables and Banach Algebras, Springer-Verlag, New York, 1998.Google Scholar
  2. [BG]Berenstein, C. A. andGay, R.,Complex Variables. An Introduction, Springer-Verlag, New York, 1991.Google Scholar
  3. [Bi]Bishop, E., Holomorphic completions, analytic continuation, and the interpolation of semi-norms,Ann. of Math. 78 (1963), 468–500.MATHMathSciNetGoogle Scholar
  4. [Br]Bremermann, H. J., On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Shilov boundaries,Trans. Amer. Math. Soc. 91 (1959), 246–276.MATHMathSciNetGoogle Scholar
  5. [Co]Coman, D., The pluricomplex Green function with two poles of the unit ball ofC n,Pacific J. Math. 194 (2000), 257–283.MATHMathSciNetGoogle Scholar
  6. [Ka]El Kasimi, A., Approximation polynômiale dans les domaines etoilés deC n,Complex Variables Theory Appl. 10 (1988), 179–182.MathSciNetGoogle Scholar
  7. [FW]Fornæss, J. E. andWiegerinck, J., Approximation of plurisubharmonic functions.Ark. Mat. 27 (1989), 257–272.MathSciNetGoogle Scholar
  8. [Hö]Hörmander, L.,An Introduction to Complex Analysis in Several Variables, 3rd ed., North-Holland, Amsterdam, 1990.Google Scholar
  9. [Ja]Jarnicki, W., Möbius function of coordinates hyperplanes in complex ellipsoids,Proc. Amer. Math. Soc. 132 (2004), 3243–3250.CrossRefMATHMathSciNetGoogle Scholar
  10. [LS1]Lárusson, F. andSigurdsson, R., Plurisubharmonic function and analytic discs on manifolds,J. Reine Angew. Math. 501 (1998), 1–39.MathSciNetGoogle Scholar
  11. [LS2]Lárusson, F. andSigurdsson, R., Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves,Indiana Univ. Math. J. 48 (1999), 1513–1534.MathSciNetGoogle Scholar
  12. [LS3]Lárusson, F. andSigurdsson, R., Erratum: Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves,Indiana Univ. Math. J. 50 (2001), 1705.MathSciNetGoogle Scholar
  13. [Ng]Nguyen, Q. D., Remarks on pluricomplex Green functions with poles along a hypersurface,Research report 21, Mid Sweden University, Sundsvall, 2000.Google Scholar
  14. [Si1]Sibony, N., Prolongement, des fonctions holomorphes bornées et metrique de Carathéodory,Invent. Math. 29 (1975), 205–230.CrossRefMATHMathSciNetGoogle Scholar
  15. [Si2]Sibony, N., Une classe de domaines pseudoconvexes,Duke Math. J. 55 (1987), 299–319.CrossRefMATHMathSciNetGoogle Scholar
  16. [Si3]Sibony, N., Some aspects of weakly pseudoconvex domains, inSeveral Complex Variables and Complex Geometry, Part 1 (Santa Cruz CA, 1989), Proc. Sympos. Pure Math.52, pp. 199–231, Amer. Math. Soc., Providence, RI, 1991.Google Scholar
  17. [Wa]Walsh, J. B., Continuity of envelopes of plurisubharmonic functions,J. Math. Mech. 18 (1968/69), 143–148.Google Scholar
  18. [Wi]Wikström, F., Jensen measures and boundary values of plurisubharmonic functions,Ark. Mat. 39 (2001), 181–200.MATHMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 2005

Authors and Affiliations

  • Quang Dieu Nguyen
    • 1
  1. 1.Department of MathematicsHanoi University of Education (Dai Hoc Su Pham Hanoi)HanoiVietnam

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