Coefficients and normal functions

Lappan, Peter

doi:10.1090/S0002-9939-1982-0656097-6

Coefficients and normal functions
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by Peter Lappan

Proc. Amer. Math. Soc. 85 (1982), 335-341

DOI: https://doi.org/10.1090/S0002-9939-1982-0656097-6

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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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