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- W14760941 abstract "The center-piece of this chapter is the following remarkable result due to Friedrich Schottky: if f is holomorphic in D(0, 1) 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 0) does not assume 1.] The principal application is the almost immediate fact that a family of holomorphic functions on a common domain, none of which has 0 or 1 in its range, if bounded at a point, is uniformly bounded in a neighborhood of that point. The compactness theorems of Chapter VII then come into play with astounding consequences. Of course “0” and “1” here are convenient normalizations: any two distinct complex numbers would serve as well." @default.
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- W14760941 date "1979-01-01" @default.
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- W14760941 title "Omitted Values and Normal Families" @default.
- W14760941 doi "https://doi.org/10.1007/978-3-0348-9374-9_13" @default.
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