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   Limit of a Blaschke product sequence
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   Author  Topic: Limit of a Blaschke product sequence  (Read 2456 times)
Sherlock
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Limit of a Blaschke product sequence  
« on: May 18th, 2006, 6:43am »
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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.
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Michael Dagg
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Re: Limit of a Blaschke product sequence  
« Reply #1 on: Jun 29th, 2006, 6:05pm »
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Sherlock, have you discovered an answer to your  
question?
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Michael Dagg
Sherlock
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Re: Limit of a Blaschke product sequence  
« Reply #2 on: Jul 3rd, 2006, 3:11am »
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Actually I haven't.  Huh Any ideas?
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Michael Dagg
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Re: Limit of a Blaschke product sequence  
« Reply #3 on: Jul 6th, 2006, 4:34pm »
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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
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