A characterization of bounded plurisubharmonic functions
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
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Pham Hoang Hiep (2005)
Annales Polonici Mathematici
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
Giorgio Patrizio (1985)
Mathematische Zeitschrift
Azimbay Sadullaev (2012)
Annales Polonici Mathematici
We consider a class of maximal plurisubharmonic functions and prove several properties of it. We also give a condition of maximality for unbounded plurisubharmonic functions in terms of the Monge-Ampère operator .
Szilárd Gy. Révész (2006)
Annales Polonici Mathematici
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...
Zbigniew Błocki (1992)
Annales Polonici Mathematici
We compute the constant sup : P a polynomial in , where S denotes the euclidean unit sphere in and σ its unitary surface measure.
Johan Thorbiörnson (1988)
Monatshefte für Mathematik
Giovanni Bassanelli (1994)
Forum mathematicum
Yang Xing (2007)
Annales Polonici Mathematici
We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.
Jean-Paul Calvi, Phung Van Manh (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
We give an elementary proof of the product formula for the multivariate transfinite diameter using multivariate Leja sequences and an identity on vandermondians.
Gregor Fels (1995)
Annales de l'institut Fourier
Let be a complex reductive group. We give a description both of domains and plurisubharmonic functions, which are invariant by the compact group, , acting on by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space . Such an invariant domain with a smooth boundary is Stein if and only if the corresponding domain is geodesically convex and the sectional curvature of its boundary fulfills the condition . The term is explicitly computable...
Urban Cegrell (2008)
Annales Polonici Mathematici
We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
Joe Callaghan (2007)
Annales Polonici Mathematici
Let K be any subset of . We define a pluricomplex Green’s function for θ-incomplete polynomials. We establish properties of analogous to those of the weighted pluricomplex Green’s function. When K is a regular compact subset of , we show that every continuous function that can be approximated uniformly on K by θ-incomplete polynomials, must vanish on . We prove a version of Siciak’s theorem and a comparison theorem for θ-incomplete polynomials. We compute when K is a compact section.
Małgorzata Zajęcka (2012)
Colloquium Mathematicae
The aim of this paper is to present an extension theorem for (N,k)-crosses with pluripolar singularities.
Thomas Bloom, Norman Levenberg, Yu. Lyubarskii (2008)
Annales de l’institut Fourier
For a regular, compact, polynomially convex circled set in , we construct a sequence of pairs of homogeneous polynomials in two variables with
Fredj Elkhadhra, Souad Mimouni (2010)
Annales de la faculté des sciences de Toulouse Mathématiques
The goal of this paper is to extend the concepts of algebraic and Liouville currents, previously defined for positive closed currents by M. Blel, S. Mimouni and G. Raby, to psh currents on . Thus, we study the growth of the projective mass of positive currents on whose support is contained in a tubular neighborhood of an algebraic subvariety. We also give a sufficient condition guaranteeing that a negative psh current is Liouville. Moreover, we prove that every negative psh algebraic current...
Urban Cegrell (1982)
Monatshefte für Mathematik
W. Plesniak (1995)
Monatshefte für Mathematik
Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)
Annales de la faculté des sciences de Toulouse Mathématiques
We prove that an analytic surface in a neighborhood of the origin in satisfies the local Phragmén-Lindelöf condition at the origin if and only if satisfies the following two conditions: (1) is nearly hyperbolic; (2) for each real simple curve in and each , the (algebraic) limit variety satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure -dimensional analytic variety to satisify .
Nguyen Quang Dieu, Tang Van Long (2007)
Annales Polonici Mathematici
Let D be a domain in ℂⁿ. We introduce a class of pluripolar sets in D which is essentially contained in the class of complete pluripolar sets. An application of this new class to the problem of approximation of holomorphic functions is also given.
Armen Edigarian (2003)
Annales Polonici Mathematici
We give a simplified proof of J. P. Rosay's result on plurisubharmonicity of the envelope of the Poisson functional [10].
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