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• 1.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
An ordering of measures induced by plurisubharmonic functions2017In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, no 3, p. 221-237Article in journal (Refereed)

We study an ordering of measures induced by plurisubharmonic functions. This ordering arises naturally in connection with problems related to negative plurisubharmonic functions. We study maximality with respect to the ordering and a related notion of minimality for certain plurisubharmonic functions. The ordering is then applied to the problem of weak*-convergence of measures, in particular Monge Ampere measures.

• 2.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Spectrum of certain Banach algebras and $\overline\partial$-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
• 3.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics. Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Spectrum of certain Banach algebras and ∂-problems2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 90, no 1, p. 51-58Article in journal (Refereed)
• 4.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
A general Dirichlet problem for the complex Monge-Ampère operator2008In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 94, no 2, p. 131-147Article in journal (Refereed)
• 5.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Potentials with respect to the pluricomplex Green function2012In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 107-111Article in journal (Refereed)

For μ a positive measure, we estimate the pluricomplex potential of μ, Pμ(x)=∫Ωg(x,y)dμ(y), where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.

• 6.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
Monge-Ampère boundary measures2009In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 2, p. 175-196Article in journal (Refereed)

We study swept-out Monge–Ampère measures of plurisubharmonic functions and boundary values related to those measures.

• 7. Czyż, Rafal
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Plurisubharmonic functions on compact sets2012In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 133-144Article in journal (Refereed)

Poletsky has introduced a notion of plurisubharmonicity for functions defined on compact sets in Cn. We show that these functions can be completely characterized in terms of monotone convergence of plurisubharmonic functions defined on neighborhoods of the compact.

• 8.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
On ordinary differentiability of Bessel potentials1984In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 44, no 3, p. 325-352Article in journal (Refereed)
• 9.
Umeå University, Faculty of Science and Technology, Mathematics and Mathematical Statistics.
A decomposition of complex Monge-Ampère measures2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 92, no 2, p. 191-195Article in journal (Refereed)
• 10.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Continuous pluriharmonic boundary values2007In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 91, p. 99-117Article in journal (Refereed)
• 11.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
On the Dirichlet problem in the Cegrell classes2004In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 84, p. 273-279Article in journal (Refereed)
• 12.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Radially symmetric plurisubharmonic functions2012In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 106, p. 1-17Article in journal (Refereed)

In this note we consider radially symmetric plurisubharmonic functions and the complex Monge–Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge–Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge–Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally we characterize radially symmetric plurisubharmonic functions among the subharmonic ones using merely the laplacian.

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