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Displaying 181 – 200 of 338

On subextension and approximation of plurisubharmonic functions with given boundary values

Hichame Amal (2014)

Annales Polonici Mathematici

Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in $_{χ} (Ω, H)$ , the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in $_{χ} (Ω, H)$ by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.

On symmetry of the pluricomplex Green function for ellipsoids

Włodzimierz Zwonek (1997)

Annales Polonici Mathematici

We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.

On the Bergman distance on model domains in ℂⁿ

Gregor Herbort (2016)

Annales Polonici Mathematici

Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in $ℂ^{n - 1}$ and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.

On the Dirichlet Problem for the Complex Monge-Ampère Operator.

Urban Cegrell (1984)

Mathematische Zeitschrift

On the Dirichlet problem in the Cegrell classes

Rafał Czyż, Per Åhag (2004)

Annales Polonici Mathematici

Let μ be a non-negative measure with finite mass given by $φ (d d^{c} ψ) ⁿ$ , where ψ is a bounded plurisubharmonic function with zero boundary values and $φ \in L^{q} ((d d^{c} ψ) ⁿ)$ , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.

On the domains of existence for plurisubharmonic functions

Urban Cegrell (1983)

Banach Center Publications

On the equivalence between locally polar and globally polar sets in $C^{n}$

J. Siciak (1983)

Banach Center Publications

On the Green function on a certain class of hyperconvex domains

Gregor Herbort (2008)

Annales Polonici Mathematici

We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate $| ψ | \leq C e x p (- C^{'} {(l o g (1 / δ_{D}))}^{α})$ at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.

On the movement of the Poincaré metric with the pseudoconvex deformation of open Riemann surfaces.

Kizuka, Takashi (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

On the multivariate transfinite diameter

Thomas Bloom, Jean-Paul Calvi (1999)

Annales Polonici Mathematici

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

On the product property for the transfinite diameter

Zbigniew Błocki, Armen Edigarian, Józef Siciak (2011)

Annales Polonici Mathematici

We give a pluripotential-theoretic proof of the product property for the transfinite diameter originally shown by Bloom and Calvi. The main tool is the Rumely formula expressing the transfinite diameter in terms of the global extremal function.

On the radius of convergence of an entire function in a normed space

C. O. Kiselman (1976)

Annales Polonici Mathematici

On the removal of subharmonic singularities of plurisubharmonic functions

E. M. Chirka (2003)

Annales Polonici Mathematici

It is proved that any subharmonic function in a domain Ω ⊂ ℂⁿ which is plurisubharmonic outside of a real hypersurface of class C¹ is indeed plurisubharmonic in Ω.

Order functions of plurisubharmonic functions

Halil Celik, Evgeny Poletsky (1997)

Studia Mathematica

We consider the following problem: find on $ℂ^{2}$ a plurisubharmonic function with a given order function. In particular, we prove that any positive ambiguous function on $ℂ ℙ^{1}$ which is constant outside a polar set is the order function of a plurisubharmonic function.

Osservazioni sulla coomologia del $\partial \bar{\partial}$

B. Bigolin (1970)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Parabolic exhaustions for strictly convex domains.

Giorgio Patrizio (1984)

Manuscripta mathematica

Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc

Siegfried Momm (1990)

Studia Mathematica

Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.

Rüdiger W. Braun, Reinhold Meise, B. Alan Taylor (2003)

RACSAM

The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood...

Plurifine potential theory

Jan Wiegerinck (2012)

Annales Polonici Mathematici

We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

Pluriharmonic extension in proper image domains

Rafał Czyż (2009)

Annales Polonici Mathematici

Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s ≥ 3. Also let $Ω_{π}$ be the image of D under the proper holomorphic map π. We characterize those continuous functions $f : \partial Ω_{π} \to ℝ$ that can be extended to a real-valued pluriharmonic function in $Ω_{π}$ .

Currently displaying 181 – 200 of 338

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