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Proceedings of the American Mathematical Society

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A bounded analytic function in the unit disk with a level set component of infinite length


Authors: K. F. Barth and J. G. Clunie
Journal: Proc. Amer. Math. Soc. 85 (1982), 562-566
MSC: Primary 30D50
DOI: https://doi.org/10.1090/S0002-9939-1982-0660605-9
MathSciNet review: 660605
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Abstract: The authors construct a bounded analytic function in the unit disk with a level set component of infinite length. The example is of the form $ \exp iB(z)$ where $ B(z)$ is a Blaschke Product.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0660605-9
Keywords: Bounded functions, level set, level curve
Article copyright: © Copyright 1982 American Mathematical Society