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Proceedings of the American Mathematical Society

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Zeros of analytic functions with infinitely differentiable boundary values


Author: James G. Caughran
Journal: Proc. Amer. Math. Soc. 24 (1970), 700-704
MSC: Primary 30.67
MathSciNet review: 0252649
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Abstract: A necessary and sufficient condition is proved that a set of points $ \{ {r_n}{e^{i\theta n}}\} $ in the unit disk be the set of zeros of an analytic function with infinitely differentiable boundary values for every choice of $ \{ {r_n}\} ,\;0 < {r_n} < 1\;{\text{and}}\;\sum {(1 - {r_n}) < \infty } $


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0252649-8
Keywords: Bounded analytic function, zero set, boundary zeros, domain with smooth boundary, Carleson set, Blaschke product
Article copyright: © Copyright 1970 American Mathematical Society