# Order functions of plurisubharmonic functions

Studia Mathematica (1997)

• Volume: 124, Issue: 2, page 161-171
• ISSN: 0039-3223

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## Abstract

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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.

## How to cite

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Celik, Halil, and Poletsky, Evgeny. "Order functions of plurisubharmonic functions." Studia Mathematica 124.2 (1997): 161-171. <http://eudml.org/doc/216405>.

@article{Celik1997,
abstract = {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 $ℂℙ^1$ which is constant outside a polar set is the order function of a plurisubharmonic function.},
author = {Celik, Halil, Poletsky, Evgeny},
journal = {Studia Mathematica},
keywords = {plurisubharmonic function; singularity; order function; $G_δ$-function},
language = {eng},
number = {2},
pages = {161-171},
title = {Order functions of plurisubharmonic functions},
url = {http://eudml.org/doc/216405},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Celik, Halil
AU - Poletsky, Evgeny
TI - Order functions of plurisubharmonic functions
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 2
SP - 161
EP - 171
AB - 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 $ℂℙ^1$ which is constant outside a polar set is the order function of a plurisubharmonic function.
LA - eng
KW - plurisubharmonic function; singularity; order function; $G_δ$-function
UR - http://eudml.org/doc/216405
ER -

## References

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1. [1] U. Cegrell and J. Thorbiörnson, Extremal plurisubharmonic functions, Ann. Polon. Math. 63 (1996), 63-69. Zbl0924.31005
2. [2] H. I. Celik, Pointwise singularities of plurisubharmonic functions, Ph.D. thesis, Syracuse Univ., 1996.
3. [3] H. I. Celik and E. A. Poletsky, Fundamental solutions of the complex Monge-Ampère equation, Ann. Polon. Math., to appear. Zbl0892.32013
4. [4] J. P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in: Complex Analysis and Geometry, Plenum Press, New York, 1993, 115-193. Zbl0792.32006
5. [5] L. Hörmander and R. Sigurdsson, Limit sets of plurisubharmonic functions, Math. Scand. 65 (1989), 308-320. Zbl0718.32016
6. [6] C. O. Kiselman, Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107 (1979), 295-304. Zbl0416.32007
7. [7] C. O. Kiselman, Plurisubharmonic functions and their singularities, in: Complex Potential Theory, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 439, Kluwer, Dordrecht, 1994, 273-323. Zbl0810.31007
8. [8] N. S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972.

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