S.O.S. Mathematics CyberBoard

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)

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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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