Logarithmic derivatives in annuli

In this paper, we define Nevanlinna functions in annuli with two independent variables and use them to prove a version of the generalized logarithmic derivative lemma in annuli. As a corollary, we can conclude the logarithmic derivative lemma in a disk and the complex plane.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-08, Vol.356 (2), p.441-452
Main Authors: Lund, Mark E., Ye, Zhuan
Format: Article
Language:English
Subjects:
Annuli
Exact sciences and technology
Functions of a complex variable
Logarithmic derivatives
Mathematical analysis
Mathematics
Meromorphic functions
Nevanlinna theory
Sciences and techniques of general use
Several complex variables and analytic spaces
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Description
Summary:In this paper, we define Nevanlinna functions in annuli with two independent variables and use them to prove a version of the generalized logarithmic derivative lemma in annuli. As a corollary, we can conclude the logarithmic derivative lemma in a disk and the complex plane.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.03.025