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   Author  Topic: convergent functions  (Read 2437 times)
tiox
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convergent functions  
« on: Mar 24th, 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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Re: convergent functions  
« Reply #1 on: Mar 24th, 2006, 3:26pm »
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Since un converges uniformly to a function u, u must be the real part of the limit of fn, 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 24th, 2006, 3:43pm by Icarus » IP Logged

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