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Omitted Values and Normal Families

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Classical Analysis in the Complex Plane

Part of the book series: Cornerstones ((COR))

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Abstract

The center-piece of this chapter is the following remarkable result due to Friedrich Schottky: if f is holomorphic in ⅅ and assumes neither of the values 0 or 1, then f is bounded in D(0, r) by a bound depending on r and |f(0)| only, for each r 1.

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Burckel, R.B. (2021). Omitted Values and Normal Families. In: Classical Analysis in the Complex Plane. Cornerstones. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-0716-1965-0_13

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