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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. Dieu, Nguyen Quang
    et al.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Jensen measures and approximation of plurisubharmonic functions2005In: Michigan Mathematical Journal, ISSN 0026-2285, Vol. 53, no 3, p. 529-544Article in journal (Refereed)
    Abstract [en]

    Let $Omega$ be a bounded domain in $Cn$. We study relations between Jensen measures for continuous and upper bounded plurisubharmonic functions on $Omega$, and give some conditions on $Omega$ that imply that these two classes of measures coincide.

  • 3.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    An extremal function for the multiplier algebra of the universal Pick space2004In: Illinois Journal of Mathematics, ISSN 0019-2082, Vol. 48, no 3, p. 1053-1065Article in journal (Refereed)
    Abstract [en]

    Let $H^2_m$ be the Hilbert function space on the unit ball in $C{m}$ defined by the kernel $k(z,w) = (1-langle z,w rangle)^{-1}$. For any weak zero set of the multiplier algebra of $H^2_m$, we study a natural extremal function, $E$. We investigate the properties of $E$ and show for example that $E$ tends to $0$ at almost every boundary point. We also give several explicit examples of the extremal function and compare the behaviour of $E$ to the behaviour of $delta^*$ and $g$, the corresponding extremal function for $H^infty$ and the pluricomplex Green function, respectively.

  • 4.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
    Area, mått och integraler2008In: Människor och matematik - läsebok för nyfikna, Göteborg: Nationellt centrum för matematikutbildning (NCM), 2008, p. 390-Chapter in book (Other (popular science, discussion, etc.))
    Abstract [sv]

    Populärvetenskaplig uppsats om det moderna areabegreppet.

  • 5.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Computing the pluricomplex Green function with two poles2003In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 12, no 3, p. 375-384Article in journal (Refereed)
    Abstract [en]

    We look at numerical computations of the pluricomplex Green function $g$ with two poles of equal weight for the bidisk. The results we obtain strongly suggest that Coman's conjecture holds in this setting, that is that $g$ equals the Lempert function. We also prove this in a special case. Furthermore, we show that Coman's conjecture fails in the case of two poles of different weight in the unit ball of $C2$.

  • 6.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Continuity of the relative extremal function on analytic varieties in C^n2005In: Annales Polonici Mathematici, ISSN 0066-2216, Vol. 86, no 3, p. 219-225Article in journal (Refereed)
    Abstract [en]

    Let $V$ be an analytic variety in a domain $Omega subset Cn$ and let $K relcomp V$ be a closed subset. By studying Jensen measures for certain classes of plurisubharmonic functions on $V$, we prove that the relative extremal function $omega_K$ is continuous on $V$ if $Omega$ is hyperconvex and $K$ is regular.

  • 7.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Jensen measures and boundary values of plurisubharmonic functions2001In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 39, no 1, p. 181-200Article in journal (Refereed)
    Abstract [en]

    We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions in B-regular domain. This theorem implies that the two classes of Jensen measures coincide in B-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above. The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function.

  • 8.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Non-linearity of the pluricomplex Green function2001In: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 129, no 4, p. 1051-1056Article in journal (Refereed)
    Abstract [en]

    We consider the pluricomplex Green function with multiple poles as introduced by Lelong. We give a partial solution to a question concerning the set where the multipole Green function coincides with the sum of the corresponding single pole Green functions.

  • 9.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Partial harmonicity of continuous maximal plurisubharmonic functions2002In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 47, no 1, p. 73-79Article in journal (Refereed)
    Abstract [en]

    If $u$ is a sufficiently smooth maximal plurisubharmonic function such that the complex Hessian of $u$ has constant rank, it is known that there exists a foliation by complex manifolds, such that $u$ is harmonic along the leaves of the foliation. In this paper, we show a partial analogue of this result for maximal plurisubharmonic functions that are merely continuous, without the assumption on the complex Hessian. In this setting, we cannot expect a foliation by complex manifolds, but we prove the existence of positive currents of bidimension $(1,1)$ such that the function is harmonic along the currents.

  • 10.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    The Dirichlet problem for maximal plurisubharmonic functions on analytic varieties in C-n2009In: International Journal of Mathematics, ISSN 0129-167X, Vol. 20, no 4, p. 521-528Article in journal (Refereed)
    Abstract [en]

    Let Omega be a B-regular domain in C-n and let V be a locally irreducible analytic variety in Omega. Given a continuous function phi is an element of C((V) over bar boolean AND partial derivative Omega), we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by f and furthermore that u is continuous on (V) over bar.

  • 11.
    Åhag, Per
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Czyz, Rafal
    Lodin, Sam
    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.
    Plurisubharmonic extension in non-degenerate analytic polyhedra2007In: Universitatis Iagellonicae Acta Mathematica, ISSN 0860-0120, no 45, p. 139-145Article in journal (Refereed)
    Abstract [en]

    Let $mathcal{P}$ be a connected, non-degenerate analytic polyhedron in $mathbb{C}^n$, $ngeq 2$. In this note we characterize those continuous functions which can be extended to a plurisubharmonic function in $mathcal{P}$.

1 - 11 of 11
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