Order functions of plurisubharmonic functions

• Autorzy: Halil Ibrahim Celik , Evgeny A. Poletsky
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

plurisubharmonic function; singularity; order function; $G_δ$-function

Kategorie tematyczne

• 31C10: Pluriharmonic and plurisubharmonic functions
• 32U05: Plurisubharmonic functions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 2
• Strony: 161-171

Daty

wydano

1997

otrzymano

1996-07-17

poprawiono

1996-12-29

Twórcy

autor

Halil Ibrahim Celik

• Department of Mathematics, Syracuse University Syracuse, New York 13244, U.S.A.

autor

Evgeny A. Poletsky

• Department of Mathematics, Syracuse University Syracuse, New York 13244, U.S.A.

Bibliografia

• [1] U. Cegrell and J. Thorbiörnson, Extremal plurisubharmonic functions, Ann. Polon. Math. 63 (1996), 63-69.
• [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.
• [4] J. P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in: Complex Analysis and Geometry, Plenum Press, New York, 1993, 115-193.
• [5] L. Hörmander and R. Sigurdsson, Limit sets of plurisubharmonic functions, Math. Scand. 65 (1989), 308-320.
• [6] C. O. Kiselman, Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107 (1979), 295-304.
• [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.
• [8] N. S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972.