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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the accumulation of the zeros of a Blaschke product at a boundary point


Author: David Protas
Journal: Proc. Amer. Math. Soc. 34 (1972), 489-496
MSC: Primary 30A72
DOI: https://doi.org/10.1090/S0002-9939-1972-0294645-2
MathSciNet review: 0294645
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Abstract: Let B be a Blaschke product with zeros $ \{ {a_n}\} $. The series $ \sum {(1 - \vert{a_n}{\vert^2})} /\vert 1 - \bar \zeta {a_n}{\vert^\gamma }$, where $ \gamma \geqq 1$ and $ \vert\zeta \vert = 1$, has been used by P. R. Ahern, D. N. Clark, G. T. Cargo, and others in the study of the boundary behavior of B and various associated functions. In this paper the convergence of this series is shown to be equivalent to a condition on a reproducing kernel for a subspace of the Hardy space $ {H^2}$. Some related conditions and corollaries are also given.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294645-2
Keywords: Blaschke product, Hardy space, inner function, invariant subspace, reproducing kernel
Article copyright: © Copyright 1972 American Mathematical Society