caa a22 4500 44586916X CHVBK 20180317145506.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00605-009-0186-z doi (NATIONALLICENCE)springer-10.1007/s00605-009-0186-z Grahl Jürgen Department of Mathematics, University of Würzburg, Würzburg, Germany aut Differential polynomials with dilations in the argument and normal families [Elektronische Daten] [Jürgen Grahl] We show that a family $${\mathcal{F}}$$ of analytic functions in the unit disk $${\mathbb{D}}$$ which satisfy a condition of the form$$ f^n(z)+P[f](xz)+b\ne 0 $$for all $${f\in\mathcal{F}}$$ and all $${z\in\mathbb{D}}$$ (where n ≥ 3, 0<|x| ≤ 1, b ≠ 0 and P is an arbitrary differential polynomial of degree at most n − 2 with constant coefficients and without terms of degree 0) is normal at the origin. Under certain additional assumptions on P the same holds also for b=0. The proof relies on a modification of Nevanlinna theory in combination with the Zalcman-Pang rescaling method. Furthermore we prove some corresponding results of Picard type for functions meromorphic in the plane. Springer-Verlag, 2010 Differential polynomials nationallicence Normal families nationallicence Nevanlinna theory nationallicence Zalcman's Lemma nationallicence Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 429-452 0026-9255 162:4<429 2011 162 605 https://doi.org/10.1007/s00605-009-0186-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-009-0186-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Grahl Jürgen Department of Mathematics, University of Würzburg, Würzburg, Germany aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 162/4(2011-04-01), 429-452 0026-9255 162:4<429 2011 162 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer