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Topic: Analytic functions (Read 10042 times) 

Elle
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I found the following problem in a complex analysis book and that's why I'm writing on this forum even if it's not really a complex analysis problem Suppose f: R > R is continuous, f^2 is real analytic and f^3 is real analytic. Prove that f is real analytic. Warning: beware of the zeros of f. All help is greatly appreciated as I'm getting a bit frustrated..


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Icarus
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Re: Analytic functions
« Reply #1 on: Dec 2^{nd}, 2005, 3:54pm » 
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I don't have time to say more, but (1) all real analytic functions are complex analytic functions restricted to the real line. (2) f = f^{3}/f^{2}. So all you have to do is show that the zeros of f^{2} induce only removable singularities in f. This is because they also must be zeros of f^{3}. All you need to do is show that they are zeros of lesser order.


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MonicaMath
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Re: Analytic functions
« Reply #2 on: Mar 2^{nd}, 2009, 10:46am » 
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so how we can do this .... ??!! can u help us more ,,,, thank you


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Eigenray
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Re: Analytic functions
« Reply #3 on: Mar 2^{nd}, 2009, 12:52pm » 
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We have two analytic functions g and h such that g^{3} = h^{2}. What can you say about their orders at a zero?


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