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One of my homework problems this week is to "characterize all holomorphic functions in $L^2(\Bbb C^n)$". I'm sorry for not being able to provide much work on my progress, but that is because I really don't know where to begin. Any help would be greatly appreciated!

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    Write down some holomorphic functions (say when $n = 1$ for simplicity) and check whether they lie in $L^2$. Repeat. Make a conjecture. See if you can prove it.2012-04-10
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    Well if a function is in $L^2(\mathbb{C}^n)$, what can you say about it as $|z| \rightarrow \infty$? Then ask yourself what holomorphic functions can satisfy such a condition.2012-04-10
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    @MichaelJoyce: I'm not sure what you're getting at but I don't think there is a simple condition satisfied by $L^2$ functions at infinity.2012-04-10
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    The mean value problem for holomorphic functions will probably be useful.2012-04-10
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    @Eric: Oops, I initially thought $L^2$ + continuous would imply bounded, but that's not the case.2012-04-10
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    A variation of Liouville's theorem2012-05-14

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