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

question?
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Regards,
Michael Dagg
Sherlock
Newbie

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

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 » Quote 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
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