Universal sequences for Zalcman's Lemma and $Q_m$-normality

• Autorzy: Shahar Nevo
• Języki publikacji: EN

Abstrakty

EN

We prove the existence of sequences ${ϱₙ}_{n=1}^∞$, ϱₙ → 0⁺, and ${zₙ}_{n=1}^∞$, |zₙ| = 1/2, such that for every α ∈ ℝ and for every meromorphic function G(z) on ℂ, there exists a meromorphic function $F(z) = F_{G,α}(z)$ on ℂ such that $ϱₙ^α F(nzₙ + nϱₙζ)$ converges to G(ζ) uniformly on compact subsets of ℂ in the spherical metric. As a result, we construct a family of functions meromorphic on the unit disk that is $Q_m$-normal for no m ≥ 1 and on which an extension of Zalcman's Lemma holds.

Kategorie tematyczne

• 30D45: Bloch functions, normal functions, normal families
• 30E10: Approximation in the complex domain

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2005
• Tom: 85
• Numer: 3
• Strony: 251-260

Daty

wydano

2005

Twórcy

autor

Shahar Nevo

• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Identyfikatory

DOI

10.4064/ap85-3-6