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 Post subject: Blaschke productPosted: Tue, 10 May 2011 07:30:06 UTC
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Joined: Sun, 13 Feb 2011 21:28:26 UTC
Posts: 25
1. let B(z) be the blaschke product for the {a_j} in D s.t. sum(1-|a_j|) < inifinty, show B has a continuous extension to P in boundary of D iff P is not an accumulation point of the a-j.

2. Now find a convergent blashcke product B(z) where no P in boundary of domain D is a regular point for B. (this is seperate from first part)

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 Post subject: Posted: Wed, 11 May 2011 02:11:27 UTC
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Joined: Sun, 13 Feb 2011 21:28:26 UTC
Posts: 25
i got the first part still not sure about the 2nd.

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 Post subject: Re: Blaschke productPosted: Wed, 11 May 2011 07:12:15 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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simba wrote:
1. let B(z) be the blaschke product for the {a_j} in D s.t. sum(1-|a_j|) < inifinty, show B has a continuous extension to P in boundary of D iff P is not an accumulation point of the a-j.

2. Now find a convergent blashcke product B(z) where no P in boundary of domain D is a regular point for B. (this is seperate from first part)

simba wrote:
i got the first part still not sure about the 2nd.

Using (1), just make every point of the circle as accumulation point, e.g. for all n.

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 Post subject: Posted: Wed, 11 May 2011 23:02:44 UTC
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Joined: Sun, 13 Feb 2011 21:28:26 UTC
Posts: 25
yea i was thinking of something like that but not sure if the infinite sum 1-|a_j| would remain convergent given all the accumulation points, the theorem is also not clear about the domain for infinite blaschke products in general. but I came up with something similar, this seems to work. thanks

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