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Proceedings of the American Mathematical Society

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

 
 

 

Power series and nonnormal functions


Authors: J. S. Hwang and Peter Lappan
Journal: Proc. Amer. Math. Soc. 97 (1986), 265-268
MSC: Primary 30D45; Secondary 30B40
DOI: https://doi.org/10.1090/S0002-9939-1986-0835877-1
MathSciNet review: 835877
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Abstract: We construct a sequence $ \left\{ {{a_n}} \right\}$ of positive numbers such that $ {a_n} \to 0,\sum {\left\vert {{a_n} - {a_{n - 1}}} \right\vert < \infty } $, and the function $ f(z) = \sum {{a_n}{z^n}} $ is not a normal function. This answers a question raised by the second author (Proc. Amer. Math. Soc. 85 (1982), 335-341).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0835877-1
Keywords: Normal function
Article copyright: © Copyright 1986 American Mathematical Society

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