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单词 PluriharmonicFunction
释义

pluriharmonic function


Definition.

Let f:Gn be a C2 (twice continuously differentiable) function. f is called pluriharmonicif for every complex line {a+bzz}the function zf(a+bz) is harmonic on the set{za+bzG}.

Note that every pluriharmonic function is a harmonic function, but not the other way around. Further it can be shown that for holomorphic functionsMathworldPlanetmath 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.

References

  • 1 Steven G. Krantz.,AMS Chelsea Publishing, Providence, Rhode Island, 1992.
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更新时间:2025/5/4 18:48:18