Order functions of plurisubharmonic functions

Halil Celik; Evgeny Poletsky

Studia Mathematica (1997)

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

Abstract

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.