A Criterion for a Meromorphic Function to be Normal
Page 1 Next
Peter Lappan (1974)
Commentarii mathematici Helvetici
Miroslav Pavlović (2008)
Czechoslovak Mathematical Journal
For a -function on the unit ball we define the Bloch norm by where is the invariant derivative of and then show that
Xinhou Hua (1995)
Manuscripta mathematica
Shanpeng Zeng, Indrajit Lahiri (2014)
Annales Polonici Mathematici
We prove a normality criterion for a family of meromorphic functions having multiple zeros which involves sharing of a non-zero value by the product of functions and their linear differential polynomials.
Maria Nowak (1995)
Banach Center Publications
Shamoyan, Romi, Li, Haiying (2010)
The Journal of Nonlinear Sciences and its Applications
Xu, Yan, Fang, Mingliang (2004)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Peter Lappan (1975)
Mathematische Zeitschrift
R. K. Kovacheva, Julian Lawrynowicz (2002)
Czechoslovak Mathematical Journal
For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best -approximation with an unbounded number of finite poles are considered.
Timoney, Richard M. (1979)
International Journal of Mathematics and Mathematical Sciences
Yasheng Ye, Xuecheng Pang, Liu Yang (2015)
Annales Polonici Mathematici
In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.
Christopher J. Bishop (1993)
Publicacions Matemàtiques
The little Bloch space, B0, is the space of all holomorphic functions f on the unit disk such that limlzl→1 lf'(z)l (1- lzl2) = 0. Finite Blaschke products are clearly in B0, but examples of infinite products in B0 are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others). Stephenson has asked whether B0 contains an infinite, indestructible Blaschke product, i.e., a Blaschke product B so that (B(z) - a)/(1 - âB(z)), is also a Blaschke...
Richard M. Timoney (1980)
Journal für die reine und angewandte Mathematik
Dubtsov, E.S. (2005)
Zapiski Nauchnykh Seminarov POMI
Kayumov, I.R. (2009)
Sibirskij Matematicheskij Zhurnal
Müller, P. F. X. (1999)
Acta Mathematica Universitatis Comenianae. New Series
Bappaditya Bhowmik, Sambhunath Sen (2024)
Czechoslovak Mathematical Journal
It is known that if is holomorphic in the open unit disc of the complex plane and if, for some , , , then . We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in . In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.
Xiao, Jie (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
J.L. Stebbins (1971)
Journal für die reine und angewandte Mathematik
Hidenobu Yoshida (1976)
Journal für die reine und angewandte Mathematik
Page 1 Next