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Journal of Mathematics and Applications

Journal of Mathematics and Applications
10/41, DOI: 10.7862/rf.2018.10

The Real and Complex Convexity

Abidi Jamel

DOI: 10.7862/rf.2018.10

Abstract

References

  1. J. Abidi, Sur quelques problèmes concernant les fonctions holomorphes et plurisousharmoniques, Rend. Circ. Mat. Palermo 51 (2002) 411-424.
  2. J. Abidi, M.L. Ben Yattou, Le minimum de deux fonctions plurisousharmoniques et une nouvelle caractérisation des fonctions holomorphes, Math. Bohem. 136 (2011) 301-310.
  3. J. Abidi, Contribution à l'étude des fonctions plurisousharmoniques convexes et analytiques, Serdica Math. J. 40 (2014) 329-388.
  4. S. Axler, P. Bourdon, W. Ramey, Harmonic Function Theory, Springer-Verlag New York, 1992.
  5. C.A. Berenstein, R. Gay, Complex Variables. An Introduction, Graduate Texts In Mathematics 125, Springer Verlag, New York, 1991.
  6. U. Cegrell, Removable singularities for plurisubharmonic functions and related problems, Proc. Lond. Math. Soc. 36 (1978) 310-336.
  7. U. Cegrell, Removable singularity sets for analytic functions having modulus with bounded Laplace mass, Proc. Amer. Math. Soc. 88 (1983) 283-286.
  8. U. Cegrell, L. Hed, Subextension and approximation of negative plurisubharmonic functions, Michigan Math. J. 56 (2008) 593-601.
  9. D. Coman, V. Guedj, A. Zeriahi, Extension of plurisubharmonic functions with growth control, J. Reine Angew. Math. 676 (2013) 33-49.
  10. J.B. Conway, Functions of One Complex Variable II, Springer-Verlag, 1995.
  11. A. Edigarian, J. Wiegerinck, The pluripolar hull of the graph of a holomorphic function with polar singularities, Indiana Univ. Math. J. 52 (2003) 1663-1680.
  12. A. Edigarian, J. Wiegerinck, Determination of the pluripolar hull of graphs of certain holomorphic functions, Ann. Inst. Fourier, Grenoble 54 (2004) 2085-2104.
  13. R.C. Gunning, H. Rossi, Analytic Functions of Several Complex Variables, Prentice - Hall, Englewood Cliffs, 1965.
  14. G.M. Henkin, J. Leiterer, Theory of Functions on Complex Manifolds, Birkhäuser, Boston, Mass., 1984.
  15. M. Hervé, Les Fonctions Analytiques, Presses Universitaires de France, 1982.
  16. L. Hörmander, An Introduction to Complex Analysis in Several Variables, Third Edition (revised), Mathematical Library, Vol. 7, North Holland, Amsterdam-New York-Oxford-Tokyo, 1990.
  17. L. Hörmander, Notions of Convexity, Birkhäuser, Basel-Boston-Berlin, 1994.
  18. J. Hyvönen, J. Rühentaus, On the extension in the Hardy classes and in the Nevanlinna class, Bull. Soc. Math. France 112 (1984) 469-480.
  19. M. Jarnicki, P. Pug, Extension of Holomorphic Functions, de Gruyter, Berlin, 2000.
  20. M. Klimek, Pluripotential Theory, Clarendon Press, Oxford, 1991.
  21. S.G. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982.
  22. F. Lárusson, R. Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998) 1-39.
  23. F. Lárusson, R. Sigurdsson, Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls, Math. Ann. 345 (2009) 159-174.
  24. P. Lelong, Fonctions Plurisousharmoniques et Formes Différentielles Positives, Gordon et Breach, New-York et Dunod, Paris, 1969.
  25. P. Lelong, Définition des fonctions plurisousharmoniques, C. R. Acad. Sci. Paris 215 (1942) 398-400.
  26. P. Lelong, Sur les suites des fonctions plurisousharmoniques, C. R. Acad. Sci. Paris 215 (1942) 454-456.
  27. P. Lelong, Les fonctions plurisousharmoniques, Ann. Sci. Ecole Norm. Sup. 62 (1945) 301-338.
  28. E. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993) 85-144.
  29. E. Poletsky, The minimum principle, Indiana Univ. Math. J. 51 (2002) 269-303.
  30. R.M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables, Springer-Verlag, 1986.
  31. J. Riihentaus, On the extension of separately hyperharmonic functions and Hp-functions, Michigan Math. J. 31 (1984) 99-112.
  32. L.I. Ronkin, Introduction to the Theory of Entire Functions of Several Variables, Amer. Math. Soc., Providence, RI 1974.
  33. W. Rudin, Function Theory in Polydiscs, Benjamin, New York, 1969.
  34. W. Rudin, Function Theory in the Unit Ball of Cn, Springer-Verlag, New York, 1980.
  35. V.S. Vladimirov, Les fonctions de plusieurs variables complexes (et leur application à la théorie quantique des champs), Paris: Dunod, 1967.

About this Article

TITLE:
The Real and Complex Convexity

AUTHORS:
Abidi Jamel

AUTHORS AFFILIATIONS:
Département de Mathématiques, Faculté des Sciences de Tunis, TUNISIA

JOURNAL:
Journal of Mathematics and Applications
10/41

KEY WORDS AND PHRASES:
Analytic; Convex and plurisubharmonic functions; Harmonic function; Inequalities; Holomorphic differential equation; Strictly; Polynomials

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/73

DOI:
10.7862/rf.2018.10

URL:
http://dx.doi.org/10.7862/rf.2018.10

RECEIVED:
2017-09-29

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