Functions of finite logarithmic order in the unit disc, Part I

The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of (usual) zero order of growth. A collection of fundamental results for meromorphic functions of finite logarithmic order is given. Some of...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 415; no. 1; pp. 435 - 461
Main Authors Heittokangas, Janne, Wen, Zhi-Tao
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2014
Subjects
Defect relation
Inverse problem
Logarithmic exponent of convergence
Logarithmic order
Meromorphic function
Nevanlinna theory
Unit disc
Logarithmic order
Logarithmic exponent of convergence
Defect relation
Nevanlinna theory
Unit disc
Meromorphic function
Inverse problem
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Summary:The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of (usual) zero order of growth. A collection of fundamental results for meromorphic functions of finite logarithmic order is given. Some of these results are reminiscent from the finite order case. Part I of this paper culminates in solving the inverse problem related to the famous defect relation in the case of finite logarithmic order. Part II deals with the analytic case.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.01.079