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plurisubharmonic function
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(Definition)
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Similarly, we could also define a plurisuperharmonic function just like we have a superharmonic function, but again it just means that  is plurisubharmonic, and so this extra term is not very useful.
Definition 2 A continuous plurisubharmonic function is said to be a pseudoconvex function.
Note that since plurisubharmonic is a long word, many authors abbreviate with psh, plsh, or plush.
- 1
- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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"plurisubharmonic function" is owned by jirka.
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(view preamble)
| Other names: |
plurisubharmonic |
| Also defines: |
plurisuperharmonic function, pseudoconvex function |
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Cross-references: continuous, superharmonic function, subharmonic function, complex line, function, upper semi-continuous
There are 6 references to this entry.
This is version 6 of plurisubharmonic function, born on 2004-07-23, modified 2006-06-18.
Object id is 6019, canonical name is PlurisubharmonicFunction.
Accessed 4171 times total.
Classification:
| AMS MSC: | 32U05 (Several complex variables and analytic spaces :: Pluripotential theory :: Plurisubharmonic functions and generalizations) | | | 31C10 (Potential theory :: Other generalizations :: Pluriharmonic and plurisubharmonic functions) |
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Pending Errata and Addenda
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