wu :: forums (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
general >> complex analysis >> Limit of a Blaschke product sequence
(Message started by: Sherlock on May 18th, 2006, 6:43am)

Title: Limit of a Blaschke product sequence
Post by Sherlock on May 18th, 2006, 6:43am
Hello everyone,

I'm puzzled by the following problem:

If a sequence {B^j} of Blaschke products
converges normally to a nonconstant holomorphic function B^0 on D, is B^0 a Blaschke product?

My hunch is that since every member of the sequence is a Blaschke product, the limit might be one as well---but maybe my thinking's too pedestrian.

Title: Re: Limit of a Blaschke product sequence
Post by Michael_Dagg on Jun 29th, 2006, 6:05pm
Sherlock, have you discovered an answer to your
question?

Title: Re: Limit of a Blaschke product sequence
Post by Sherlock on Jul 3rd, 2006, 3:11am
Actually I haven't.  ??? Any ideas?

Title: Re: Limit of a Blaschke product sequence
Post by Michael_Dagg on Jul 6th, 2006, 4:34pm
The functions  (z - 1/n)/(z/n - 1)  are Blaschke products
and converge uniformly in   D  to  -z,   which is a Blaschke product.

The result is different on   D   bar (equivalent to norm
convergence in L^{\infty} of the boundary).  



Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board