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pluriharmonic function
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(Definition)
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Note that every pluriharmonic function is a harmonic function, but not the other way around. Further it can be shown that for holomorphic functions of several complex variables the real (and the imaginary) parts are locally pluriharmonic functions. Do note however that just because a function is harmonic in each variable separately does not imply that it is pluriharmonic.
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- Steven G. Krantz. Function Theory of Several Complex Variables, AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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"pluriharmonic function" is owned by jirka.
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(view preamble)
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pluriharmonic |
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Cross-references: imply, variable, imaginary, real, several complex variables, holomorphic functions, harmonic function, harmonic, complex line, function, continuously differentiable
This is version 4 of pluriharmonic function, born on 2004-07-23, modified 2005-03-07.
Object id is 6017, canonical name is PluriharmonicFunction.
Accessed 1827 times total.
Classification:
| AMS MSC: | 31C10 (Potential theory :: Other generalizations :: Pluriharmonic and plurisubharmonic functions) | | | 32A50 (Several complex variables and analytic spaces :: Holomorphic functions of several complex variables :: Harmonic analysis of several complex variables) | | | 31C05 (Potential theory :: Other generalizations :: Harmonic, subharmonic, superharmonic functions) |
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Pending Errata and Addenda
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