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  • 1.
    Carlehed, Magnus
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function1999In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 71, no 1, p. 87-103Article in journal (Refereed)
    Abstract [en]

    We characterise hyperconvexity in terms of Jensen measures with barycentre at a boundary point. We also give an explicit formula for the pluricomplex Green function in the Hartogs' triangle. Finally we study the behaviour of the pluricomplex Green function $g(z,w)$ as the pole $w$ tends to a boundary point.

  • 2. Carlsson, Linus
    et al.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Fällström, Anders
    Spectrum of certain Banach algebras and б-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
  • 3.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    A comparison priciple for the complex Monge-Ampere operator2003Book (Other academic)
    Abstract [en]

    A comparison priniple for the complex Monge-Ampere operator

  • 4.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    A general Dirichlet problem for the Complex Monge-Ampere operator2006Report (Other academic)
  • 5.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Approximation of plurisubharmonic functions in hyperconvex domains2006Report (Other academic)
  • 6.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Boundary values of plurisubharmonic functions2004Book (Other academic)
  • 7.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Boundary values of plurisubharmonic functions and a general Dirichlet problem for the complex Monge-Amp`ere operator2005Book (Other academic)
    Abstract [en]

    Boundary values of plurisubharmonic functions and a general Dirichlet problem for the Complex Monge-Amp`ere operator. Research reports, No 1, 2005. Mid Sweden Univ.

  • 8.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Convergence in capacity2001Report (Other academic)
    Abstract [en]

    Convergence in capacity

  • 9.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Potentials with respect to the pluricomplex Green function2006Report (Other academic)
  • 10.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    The general definition of the complex Monge-Ampere operator2004In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 54, no 1, p. 159-179Article in journal (Refereed)
    Abstract [en]

    We define and study the domain of definition for the complex Monge-Ampere operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain "test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.

  • 11.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    The gradient lemma2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 91, no 2-3, p. 143-146Article in journal (Refereed)
    Abstract [en]

    We show that if a decreasing sequence of subharmonic functions converges to a function in W-loc(1,2) then the convergence is in W-loc(1,2) .

  • 12.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Weak*-convergence of Monge-Amp`ere measures2005Book (Other academic)
    Abstract [en]

    Weak*-convergence of Monge-Amp`ere measures. Research reports, No 3, 2005. Mid Sweden Univ.

  • 13.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Weak*-convergence of Monge-Amp`ere measures2006In: Mathematische Zeitschrift, ISSN 0025-5874, Vol. 254, no 3, p. 505-508Article in journal (Refereed)
    Abstract [en]

    We study the convergence of sequences of Monge-Ampère measures (dd c u j ) n where (u j ) is a given sequence of plurisubharmonic functions. Our main theorem is about approximation by multipole pluricomplex Green functions.

  • 14.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Kolodziej, Slawomir
    Zeriahi, Ahmed
    Subextension of plurisubharmonic functions with weak singularities2005In: Mathematische Zeitschrift, ISSN 1432-1823, Vol. 250, no 1, p. 7-22Article in journal (Refereed)
  • 15.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics. Department of Mathematics, Umeå University, Umeå.
    Kołodziej, Slawomir
    Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland.
    The equation of complex Monge-Amp`ere type and stability of solutions2003In: Mathematische Annalen, ISSN 0025-5831, Vol. 334, no 4, p. 713-729Article in journal (Refereed)
    Abstract [en]

    We prove that in a family of plurisubharmonic functions with Monge-Ampère measures bounded from above by such a measure of one function weak convergence is equivalent to convergence in capacity. We also show a very general statement on the existence of solutions of the complex Monge-Ampère type equation.

  • 16.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Wiklund, J
    A Monge-Ampere norm for Delta-plurisubharmonic functions2004Report (Other academic)
  • 17.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Wiklund, Jonas
    A Monge-Ampere norm for Delta-plurisubharmonic functions2005In: Mathematica Scandinavica, ISSN 0025-5521, Vol. 97, no 2, p. 201-216Article in journal (Refereed)
    Abstract [en]

    We consider differences of plurisubharmonic functions in the energy classF as a linear space, and equip this space with a norm, depending on the generalized complex Monge-Ampère operator, turning the linear space into a Banach space δF. Fundamental topological questions for this space is studied, and we prove that δF is not separable. Moreover we investigate the dual space. The study is concluded with comparison between δF and the space of delta-plurisubharmonic functions, with norm depending on the total variation of the Laplace mass, studied by the first author in an earlier paper

  • 18.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Yamaguchi, Hiroshi
    Representation of magnetic fields by jump theorem for harmonic forms2008In: Mathematical Proceedings of the Royal Irish Academy, 2008, Vol. 108, no 1, p. 7-17Conference paper (Other academic)
    Abstract [en]

    It has previously been shown that a surface current density J on a closed surface § of class C1 in R3 induces a static magnetic ¯eld BJ in R3 n §, which has some discontinuity along §. In this note, we represent BJ by use of jump theorem for harmonic forms in the case where § is of class C!.We then apply this result to prove the existence of a surface current density J, which induces the nonzero magnetic ¯eld BJ such that BJ ´ 0 inside (or outside) of the domain bounded by § in R3. This has previously been called the equilibrium magnetic ¯eld for §.

  • 19.
    Cegrell, Urban
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Zeriahi, Ahmed
    Subextension of plurisubharmonic functions with bounded Monge-Ampere mass.2003In: Comptes Rendus Mathématique. Académie des Sciences., ISSN 1631-073X, Vol. 336, no 4, p. 305-308Article in journal (Refereed)
    Abstract [en]

    Subextension of plurisubharmonic functions with bounded Monge-Ampere mass.

  • 20.
    Åhag, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Cegrell, Urban
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Hoang Hiep, Pham
    Truong Dai Hoc Su Pham Ha Noi, Dept Math, Hanoi, Vietnam.
    A PRODUCT PROPERTY FOR THE PLURICOMPLEX ENERGY2010In: Osaka Journal of Mathematics, ISSN 0030-6126, Vol. 47, no 3, p. 637-650Article in journal (Refereed)
    Abstract [en]

    In this note we prove a product property for the pluricomplex energy, and then give some applications.

1 - 20 of 20
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