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Bloch's principle and normal criterion - MaRDI portal

Bloch's principle and normal criterion (Q1262969)

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scientific article; zbMATH DE number 4125755
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Bloch's principle and normal criterion
scientific article; zbMATH DE number 4125755

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    Bloch's principle and normal criterion (English)
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    1989
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    \textit{L. Zalcman} [Am. Math. Monthly 82, 813-817 (1975; Zbl 0315.30036)] gave a precise form of the heuristic principle that ``a family of holomorphic functions which have a common property \(P\) in a domain \(D\) is (apt to be) a normal family in \(D\) if \(P\) cannot be possessed by a non-constant entire function in the finite plane''. The author uses a modified version of Zalcman's principle to establish the normality of the family \(F\) of meromorphic functions \(f(z)\) satisfying \(f^ nf'\neq 1\) (\(n\geq 2\)) in a domain \(D\).
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    Bloch's principle
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    normal family
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