A bounded plurisubharmonic function which is not an infinite sum of continuous plurisubharmonic functions (Q5951874)
From MaRDI portal
scientific article; zbMATH DE number 1687374
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bounded plurisubharmonic function which is not an infinite sum of continuous plurisubharmonic functions |
scientific article; zbMATH DE number 1687374 |
Statements
A bounded plurisubharmonic function which is not an infinite sum of continuous plurisubharmonic functions (English)
0 references
10 October 2002
0 references
It is known that in the unit disc, every bounded subharmonic function is an (infinite) sum of continuous subharmonic functions. The author constructs a bounded plurisubharmonic function in the unit bidisc, which cannot be represented, in a smaller bidisc, as a sum of continuous plurisubharmonic functions. This answers a question from [\textit{U. Cegrell} and \textit{J. Thorbiörnson}, Ann. Pol. Math. 63, No. 1, 63-69 (1996; Zbl 0924.31005)].
0 references
bounded plurisubharmonic function
0 references
unit bidisc
0 references
