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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a problem of Berman concerning radial limits


Authors: J. S. Hwang and Peter Lappan
Journal: Proc. Amer. Math. Soc. 95 (1985), 155-156
MSC: Primary 30D40; Secondary 30D50
MathSciNet review: 796466
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Abstract: Given a $ {G_\delta }$-subset $ E$ of the unit circle $ T$ such that $ E$ is of measure zero, we prove that there exists a nonvanishing function $ g \in {H^\infty }$ such that $ g(z)$ has a radial limit at each point of $ T$ and this radial limit is zero at each point of $ E$. This answers a problem of R. Berman (Proc. Amer. Math. Soc. 92 (1984), 64-66).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0796466-X
PII: S 0002-9939(1985)0796466-X
Keywords: Radial limit
Article copyright: © Copyright 1985 American Mathematical Society