Normal Families of Meromorphic Functions in Several Variables

We extend the well-known Gu’s normality criterion for meromorphic functions of one complex variable to the case of several complex variables. Let F be a family of functions meromorphic on a given domain D ⊂ C n , k a positive integer and a ∈ ( C \ { 0 } ) n a point. If for every function f ∈ F , all...

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Vydané v:Computational methods and function theory Ročník 24; číslo 3; s. 457 - 477
Hlavní autori: Chang, Jianming, Xu, Yan, Yang, Liu
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2024
Predmet:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Normal family
Several variables
32A19
30D35
32A20
Meromorphic function
ISSN:1617-9447, 2195-3724
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Popis
Shrnutí:We extend the well-known Gu’s normality criterion for meromorphic functions of one complex variable to the case of several complex variables. Let F be a family of functions meromorphic on a given domain D ⊂ C n , k a positive integer and a ∈ ( C \ { 0 } ) n a point. If for every function f ∈ F , all of its zeros have multiplicity at least k + 2 and the partial derivatives ∇ k f ≠ a on D , then the family F is normal in D .
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-023-00502-7