Showing papers by "Lawrence Zalcman published in 2005"
TL;DR: In this article, a family of meromorphic functions on the plane domain D, all of whose zeros and poles are multiple, is considered. And if for each f ∈ f, f'(z) ¬= h(z), for z ∈ D, then J is normal on D.
Abstract: Let y be a family of meromorphic functions on the plane domain D, all of whose zeros and poles are multiple. Let h be a meromorphic function which does not vanish on D. If for each f ∈ f, f'(z) ¬= h(z) for z ∈ D, then J is normal on D.
16 citations
TL;DR: In this article, a quasinormal family of meromorphic functions on D, all of whose zeros are multiple, and ϕ being a holomorphic function univalent on D are considered.
Abstract: Let \(F\) be a quasinormal family of meromorphic functions on D, all of whose zeros are multiple, and let ϕ be a holomorphic function univalent on D. Suppose that for any f ∊ \(F\) , f′(z) ≠ ϕ′(z) for z ∊ D. Then \(F\) is quasinormal of order 1 on D. Moreover, if there exists a compact set K ⊂ D such that each f ∊ \(F\). vanishes at two distinct points of K, then \(F\) is normal on D.
15 citations
TL;DR: In this article, a new and simplified proof of a result of Pang and Zalcman concerning normality and, shared values is given, and the number 3 is shown to be the best possible.
Abstract: LetF be families of meromorphic functions in a domainD, and letR be a rational function whose degree is at least 3. If, for anyf∈F, the composite functionR(f) has no fixed-point inD, thenF is normal inD. The number 3 is best possible. A new and much simplified proof of a result of Pang and Zalcman concerning normality and, shared values is also given.
11 citations
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TL;DR: In this article, the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain was studied, and an angle distortion theorem for starlike and spirallike functions with respect to interior and boundary points was proved.
Abstract: In this paper, we study conditions which ensure the existence of backward flow invariant domains for semigroups of holomorphic self-mappings of a simply connected domain $D$. More precisely, the problem is the following. Given a one-parameter semigroup $\mathcal S$ on $D$, find a simply connected subset $\Omega\subset D$ such that each element of $\mathcal S$ is an automorphism of $\Omega$, in other words, such that $\mathcal S$ forms a one-parameter group on $\Omega$.
On the way to solving this problem, we prove an angle distortion theorem for starlike and spirallike functions with respect to interior and boundary points.
7 citations
TL;DR: In this article, the authors present a derivation of Qôs, the name of the chief god of the Edomites, from the Arabic qaus, ''bow,« but rather from West Semitic qws, ''feel a sickening dread,« and is thus a close equivalent of Paḥad Yiṣḥaq, ''Fear of Isaac«.
Abstract: Abstract Qôs, the name of the chief god of the Edomites, is not to be derived (as commonly thought) from the Arabic qaus, »bow,« but rather from West Semitic qws, »feel a sickening dread,« and is thus a close equivalent of Paḥad Yiṣḥaq, »Fear of Isaac«. This derivation lends support to A. Alt’s suggestion of a common Israelite-Edomite cultic center at Beersheba devoted to the worship of Paḥad Yiṣḥaq and also offers new perspectives on Jer 49,16 and II Chr 25,14–15. Qôs, der Name des Hauptgottes der Edomiter, ist nicht (wie gewöhnlich angenommen wird) vom arabischen qaus, »Bogen«, herzuleiten, sondern vielmehr vom westsemitischen qws, »einen krankmachenden Schrecken fühlen«. So stellt er ein nahes Äquivalent von Paḥad Yiṣḥaq, »Schrecken Isaaks« dar. Diese Herleitung unterstützt A. Alts Vorschlag von einem gemeinsamen israelitisch-edomitischen Kultzentrum in Beerscheba, das der Verehrung von Paḥad Yiṣḥaq diente, und eröffnet auch neue Perspektiven für Jer 49,16 and II Chr 25,14–15. Qôs, le nom du dieu principal des Édomites, n’est pas à dériver (ainsi qu’il est admis le plus souvent) de l’arabe qaus – »arc«, mais plutôt de la racine ouest-sémitique qws – »ressentir un effroi qui rend malade«. Ce nom représente ainsi un équivalent proche de: Paḥad Yiṣḥaq, »Effroi d’Isaac«. Cette origine conforte l’hypothèse d’A. Alt concernant un centre cultuel commun, des Israélites et des Édomites, à Beer-Shéba, qui était voué à la vénération de Paḥad Yiṣḥaq et qui ouvre de nouvelles perspectives pour la compréhension de Jér 49,16 et de II Chr 25,14–15.
3 citations