wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        general >> complex analysis >> convergent functions
        
(Message started by: tiox on Mar 24^th, 2006, 1:58pm)

Title: convergent functions
Post by tiox on Mar 24^th, 2006, 1:58pm

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.

Title: Re: convergent functions
Post by Icarus on Mar 24^th, 2006, 3:26pm

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?