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Transactions of the American Mathematical Society

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Studies of Differences from the point of view of Nevanlinna Theory


Authors: Zheng Jianhua and Risto Korhonen
Journal: Trans. Amer. Math. Soc. 373 (2020), 4285-4318
MSC (2010): Primary 39A10; Secondary 30D35, 39A12
DOI: https://doi.org/10.1090/tran/8069
Published electronically: March 10, 2020
MathSciNet review: 4105524
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Abstract: This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic derivative of a $\delta$-subharmonic function is established allowing the case of hyper-order equal to one and minimal hyper-type, which improves the condition of the hyper-order less than one. Finally, we make a careful discussion of a well-known difference equation and give the possible forms of the equation under a growth condition for the solutions.


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Additional Information

Zheng Jianhua
Affiliation: Department of Mathematical Sciences, Tsinghua University, People’s Republic of China
Email: zheng-jh@mail.tsinghua.edu.cn

Risto Korhonen
Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P. O. Box 111, 80101 Joensuu, Finland
MR Author ID: 702144
Email: risto.korhonen@uef.fi

Received by editor(s): August 2, 2018
Received by editor(s) in revised form: June 19, 2019, and October 14, 2019
Published electronically: March 10, 2020
Additional Notes: The first author was partially supported by the grant (No. 11571193) of NSF of China.
The second author was supported in part by the Academy of Finland grant 286877.
Article copyright: © Copyright 2020 American Mathematical Society