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Topic: Limit of a Blaschke product sequence (Read 2468 times) |
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Sherlock
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Posts: 2
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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
Senior Riddler
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Posts: 500
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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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Regards,
Michael Dagg
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Sherlock
Newbie
Posts: 2
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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.  Any ideas?
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Michael Dagg
Senior Riddler
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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).
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| « Last Edit: Jul 6th, 2006, 7:02pm by Michael Dagg » |
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Regards,
Michael Dagg
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