Talk:Plurisubharmonic function
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Merging to harmonic function?
I think this page should be either extended or what I 'd prefer most intergrated in the 'subharmonic'-Entry. Hottiger 21:17, 8 March 2006 (UTC)
- Good point about this article being rather stubby. As history has it, this article was created before the one on subharmonic function, and that may explain why it was not merged to start with.
- Now, I would think it would be fine if it stays the way it is. This article is indeed rather small, but on the other hand the one at subharmonic function is big enough, and in my view, it would be easier to read the subharmonic function without having to even think of n complex dimensions, which may be intimidating. :)
- I would be more than happy if some expert (I am not) would extend this one. Oleg Alexandrov (talk) 21:57, 8 March 2006 (UTC)
Sandbox for entirely revised entry
Note: This is only the very beginning of some reformulation.
In mathematics, plurisubharmonic functions form an important class of functions used in complex analysis. They are the higher dimensional generalization of subharmonic functions. They can be defined in full generality on complex spaces.
Formal definition
Let is any complex space and denote the unit disk. Then a upper semi-continuus function function
is said plurisubharmonic if and only if for any holomorphic map the function
is subharmonic.