montel’s theorem
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Author(s):  
THIERRY MEYRATH ◽  
JÜRGEN MÜLLER

Abstract We investigate the behaviour of families of meromorphic functions in the neighbourhood of points of non-normality and prove certain covering properties that complement Montel’s Theorem. In particular, we also obtain characterisations of non-normality in terms of such properties.



2016 ◽  
Vol 107 (5) ◽  
pp. 511-521
Author(s):  
Gopal Datt ◽  
Sanjay Kumar
Keyword(s):  


2016 ◽  
Vol 106 (3) ◽  
pp. 257-263
Author(s):  
Kuldeep Singh Charak ◽  
Virender Singh


2015 ◽  
Vol 31 (1) ◽  
pp. 1-10
Author(s):  
J. M. ALMIRA ◽  
◽  
KH. F. ABU-HELAIEL ◽  

Recently, the first author of this paper, used the structure of finite dimensional translation invariant subspaces of C(R, C) to give a new proof of classical Montel’s theorem, about continuous solutions of Frechet’s functional equation ∆m h f = 0, for real functions (and complex functions) of one real variable. In this paper we use similar ideas to prove a Montel’s type theorem for the case of complex valued functions defined over the discrete group Z d. Furthermore, we also state and demonstrate an improved version of Montel’s Theorem for complex functions of several real variables and complex functions of several complex variables.





2012 ◽  
Vol 148 (3) ◽  
pp. 966-990 ◽  
Author(s):  
Charles Favre ◽  
Jan Kiwi ◽  
Eugenio Trucco

AbstractWe prove a version of Montel’s theorem for analytic functions over a non-Archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-Archimedean entire functions.



2005 ◽  
Vol 305 (2) ◽  
pp. 743-751 ◽  
Author(s):  
Yan Xu
Keyword(s):  


2002 ◽  
Vol 52 (3) ◽  
pp. 483-498
Author(s):  
R. K. Kovacheva ◽  
J. Lawrynowicz


2002 ◽  
Vol 115 (1) ◽  
pp. 56-71 ◽  
Author(s):  
R.K. Kovacheva ◽  
J. Ławrynowicz


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