Universal sequences for Zalcman's Lemma and Q~ m-normality

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We prove the existence of sequences {ρn}∞ n=1, ρn → 0 +, |zn| = 1 2 , such that for every α ∈ R and for every meromorphic function G(z) on C, there exists a corresponding meromorphic function F(z) = FG,α(z) on C, such that ρ α nF(nzn + nρnζ) χ⇒ G(ζ) on C. As a result, we construct a family of functions meromorphic on the unit disk ∆ that is not Qm-normal for every m ≥ 1 and on which an extension of Zalcman's Lemma holds.
Original languageAmerican English
Pages (from-to)251-260
JournalAnnales Polonici Mathematici
Issue number3
StatePublished - 2005


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