# Order functions of plurisubharmonic functions

Studia Mathematica (1997)

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

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topCelik, 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

top- [1] U. Cegrell and J. Thorbiörnson, Extremal plurisubharmonic functions, Ann. Polon. Math. 63 (1996), 63-69. Zbl0924.31005
- [2] H. I. Celik, Pointwise singularities of plurisubharmonic functions, Ph.D. thesis, Syracuse Univ., 1996.
- [3] H. I. Celik and E. A. Poletsky, Fundamental solutions of the complex Monge-Ampère equation, Ann. Polon. Math., to appear. Zbl0892.32013
- [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] L. Hörmander and R. Sigurdsson, Limit sets of plurisubharmonic functions, Math. Scand. 65 (1989), 308-320. Zbl0718.32016
- [6] C. O. Kiselman, Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107 (1979), 295-304. Zbl0416.32007
- [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] N. S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972.

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