Zeros of analytic functions with infinitely differentiable boundary values

Caughran, James G.

doi:10.1090/S0002-9939-1970-0252649-8

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
DOI: https://doi.org/10.1090/S0002-9939-1970-0252649-8
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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