Author 
Topic: convergent functions (Read 2437 times) 

tiox
Newbie
Posts: 2


convergent functions
« on: Mar 24^{th}, 2006, 1:58pm » 
Quote Modify

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.


IP Logged 



Icarus
wu::riddles Moderator Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863


Re: convergent functions
« Reply #1 on: Mar 24^{th}, 2006, 3:26pm » 
Quote Modify

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 » 
IP Logged 
"Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? "  Anonymous



