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Topic: convergent functions (Read 2591 times) 

tiox
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convergent functions
« on: Mar 24^{th}, 2006, 1:58pm » 
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Could someone give me a hint on this? Suppose f_n are analytic in a region D, u_n is the real part of f_n, and u_n converges uniformly con compact subsets of D. Show that if f_n(z) converges for at least one z, then f_n converges uniformly on compact subsets of D.


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Icarus
wu::riddles Moderator Uberpuzzler
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Re: convergent functions
« Reply #1 on: Mar 24^{th}, 2006, 3:26pm » 
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Since u_{n} converges uniformly to a function u, u must be the real part of the limit of f_{n}, should that sequence also converge. All you can be sure of about u is that it is continuous, and therefore integrable. Can you find a way of expressing v in terms of the integral of an expression involving u?

« Last Edit: Mar 24^{th}, 2006, 3:43pm by Icarus » 
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