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arXiv · 1709.05034

Radially distributed values and normal families

Walter Bergweiler·Alexandre Eremenko
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Abstract

Let $L_0$ and $L_1$ be two distinct rays emanating from the origin and let ${\mathcal F}$ be the family of all functions holomorphic in the unit disk ${\mathbb D}$ for which all zeros lie on $L_0$ while all $1$-points lie on $L_1$. It is shown that ${\mathcal F}$ is normal in ${\mathbb D}\backslash\{0\}$. The case where $L_0$ is the positive real axis and $L_1$ is the negative real axis is studied in more detail.

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Walter Bergweiler, Alexandre Eremenko. 2018-01-03. Radially distributed values and normal families. https://doi.org/10.1093/imrn%2Frny005

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