Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 10

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

The complex Monge-Ampère operator in the Cegrell classes

100%
Czyż R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
The complex Monge-Ampère operator is a useful tool not only within pluripotential theory, but also in algebraic geometry, dynamical systems and Kähler geometry. In this self-contained survey we present a unified theory of Cegrell's framework for the complex Monge-Ampère operator.
2
Content available remote

The complex Monge-Ampère equation for complex homogeneous functions in ℂⁿ

95%
Czyż R.
Annales Polonici Mathematici
|
2001
|
tom 76
|
nr 3
287-302
EN
We prove some existence results for the complex Monge-Ampère equation $(dd^cu)ⁿ = gdλ$ in ℂⁿ in a certain class of homogeneous functions in ℂⁿ, i.e. we show that for some nonnegative complex homogeneous functions g there exists a plurisubharmonic complex homogeneous solution u of the complex Monge-Ampère equation.
3
Content available remote

On a Monge-Ampère type equation in the Cegrell class $𝓔_{χ}$

95%
Czyż R.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 1
89-97
EN
Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation $-χ(u)(dd^cu)ⁿ = dμ$. Under some additional assumption the solution u is uniquely determined.
4
Content available remote

Pluriharmonic extension in proper image domains

95%
Czyż R.
Annales Polonici Mathematici
|
2009
|
tom 96
|
nr 2
163-174
EN
Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D₁ ×⋯× D_{s}$, 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 $f:∂Ω_π → ℝ$ that can be extended to a real-valued pluriharmonic function in $Ω_π$.
5
Content available remote

On the Dirichlet problem in the Cegrell classes

61%
Czyż R., Åhag P.
Annales Polonici Mathematici
|
2004
|
tom 84
|
nr 3
273-279
EN
Let μ be a non-negative measure with finite mass given by $φ(dd^{c}ψ)ⁿ$, where ψ is a bounded plurisubharmonic function with zero boundary values and $φ ∈ L^{q}((dd^{c}ψ)ⁿ)$, φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.
6
Content available remote

Subextension of plurisubharmonic functions without increasing the total Monge-Ampère mass

61%
Czyż R., Hed L.
Annales Polonici Mathematici
|
2008
|
tom 94
|
nr 3
275-281
EN
We prove that subextension of certain plurisubharmonic functions is always possible without increasing the total Monge-Ampère mass.
7
Content available remote

Continuous pluriharmonic boundary values

61%
Åhag P., Czyż R.
Annales Polonici Mathematici
|
2007
|
tom 91
|
nr 2-3
99-117
EN
Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D₁ × ⋯ × D_{s}$, j=1,...,s, s≥ 3. Also let 𝔾ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or 𝔾ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.
8
Content available remote

Radially symmetric plurisubharmonic functions

49%
Åhag P., Czyż R., Persson L.
Annales Polonici Mathematici
|
2012
|
tom 106
|
nr 1
1-17
EN
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.
9
Content available remote

Plurisubharmonic functions on compact sets

49%
Czyż R., Hed L., Persson H.
Annales Polonici Mathematici
|
2012
|
tom 106
|
nr 1
133-144
EN
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.
10
Content available remote

Concerning the energy class $𝓔_p$ for 0 < p < 1

49%
Åhag P., Czyż R., Hiêp P.
Annales Polonici Mathematici
|
2007
|
tom 91
|
nr 2-3
119-130
EN
The energy class $𝓔_{p}$ is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of $ℱ_{p}$ and its pluricomplex p-energy is proved.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.