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        general >> complex analysis >> entire function and polynoials
        
(Message started by: MonicaMath on Feb 26th, 2009, 11:56am)
Title: entire function and polynoials
Post by MonicaMath on Feb 26th, 2009, 11:56am
Hi everybody...

I have a BIG problem that needs to solve:

if f(z) is an entire function with |f(z)<=B|z|^S, for all z in C,
(1) Should S be an integer and why,
(2) can we write f  as: f(z)=A z^j, for some A in C, with |A|<=B.

please can one help me in soving this problem.
Title: Re: entire function and polynoials
Post by Eigenray on Feb 26th, 2009, 7:56pm
The conclusion should be that f(z) is a polynomial of degree no more than S.

Are you familiar with [link=http://en.wikipedia.org/wiki/Liouville%27s_theorem_(complex_analysis)]Liouville's theorem[/link]?  Try to generalize the proof there to show that ak = 0 for k > S.


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