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Proceedings of the American Mathematical Society

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

 
 

 

Coefficients and normal functions


Author: Peter Lappan
Journal: Proc. Amer. Math. Soc. 85 (1982), 335-341
MSC: Primary 30D45
DOI: https://doi.org/10.1090/S0002-9939-1982-0656097-6
MathSciNet review: 656097
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Abstract: Let $f(z) = \sum {a_n}{z^n}$ be an analytic function in the unit disc. It is proved that if $\{ {a_n}\}$ is a bounded monotone sequence of real numbers, or if $\sum |{a_n} - {a_{n - 1}}| < \infty$ and ${a_n} \nrightarrow 0$, then $f(z)$ is a normal function. Examples are given to show that these results are delicate.


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Keywords: Normal function, nonnormal point
Article copyright: © Copyright 1982 American Mathematical Society