Abstract
The aim of this paper is to provide a quantitative version of a normality criterion recently given by Grahl and Nevo [GN] and a new proof of it based on the Schwarzian derivative and associated linear differential equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. V. Ahlfors, Complex Analysis, third edition, McGraw-Hill, 1979.
P. L. Duren, Univalent Functions, Springer, 1983.
J. Grahl and S. Nevo, A note on spherical derivatives and normal families, J. Anal. Math. 117 (2012), 119–128.
E. Hille, Remarks on a paper by Zeev Nehari, Bull. Amer. Math. Soc. 55 (1949), 552–553.
E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, 1969.
Z. Nehari, The Schwarzian derivative and schlicht functions, Bull. Amer. Math. Soc. 55 (1949), 544–551.
R. Nevanlinna, Eindeutige analytische Funktionen, Springer 1936.
L. Zalcman, A heuristic principle in complex function theory, Amer. Math. Monthly 82 (1975), 813–817.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Steinmetz, N. Normal families and linear differential equations. JAMA 117, 129–132 (2012). https://doi.org/10.1007/s11854-012-0017-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11854-012-0017-3