wu :: forums
wu :: forums - Limit of a Blaschke product sequence

Welcome, Guest. Please Login or Register.
Mar 28th, 2023, 5:23am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   general
   complex analysis
(Moderators: ThudnBlunder, Icarus, Grimbal, Eigenray, SMQ, towr, william wu)
   Limit of a Blaschke product sequence
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Limit of a Blaschke product sequence  (Read 2320 times)
Sherlock
Newbie
*





   


Posts: 2
Limit of a Blaschke product sequence  
« on: May 18th, 2006, 6:43am »
Quote Quote Modify Modify

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.
IP Logged
Michael Dagg
Senior Riddler
****






   


Gender: male
Posts: 500
Re: Limit of a Blaschke product sequence  
« Reply #1 on: Jun 29th, 2006, 6:05pm »
Quote Quote Modify Modify

Sherlock, have you discovered an answer to your  
question?
IP Logged

Regards,
Michael Dagg
Sherlock
Newbie
*





   


Posts: 2
Re: Limit of a Blaschke product sequence  
« Reply #2 on: Jul 3rd, 2006, 3:11am »
Quote Quote Modify Modify

Actually I haven't.  Huh Any ideas?
IP Logged
Michael Dagg
Senior Riddler
****






   


Gender: male
Posts: 500
Re: Limit of a Blaschke product sequence  
« Reply #3 on: Jul 6th, 2006, 4:34pm »
Quote Quote Modify Modify

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).  
« Last Edit: Jul 6th, 2006, 7:02pm by Michael Dagg » IP Logged

Regards,
Michael Dagg
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

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