to show entire holomorphic function is constant

Asked Feb 02 '13 at 03:54

Active Feb 02 '13 at 03:54

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An entire function with periodic bounds

$f(z)$ is an entire holomorphic function, $f(z)=f(z+1)$ and $|f(z)| \leq e^{|z|}$ then how can we show that $f$ is constant? (without using extension theorem)

Indeed this question was asked before, but is there any alternative approach?

edited Apr 13 '17 at 12:20

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asked Feb 02 '13 at 03:54

wqr

Would you be able to explain what the Extension Theorem is? – Haskell Curry Feb 02 '13 at 04:27
I meant Riemann's extension theorem. – wqr Feb 02 '13 at 04:56
"Indeed this question was asked before:" Would you please provide a link? If you are referring to this, will you please elaborate on what you are looking for that isn't found there? – Jonas Meyer Feb 02 '13 at 06:38

to show entire holomorphic function is constant

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