On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane

doi:10.1007/s11139-007-9101-1

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	On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane
	Chiang, Yik-Man 1; Feng, Shao-Ji2
	2008-05-01
发表期刊	RAMANUJAN JOURNAL
ISSN	1382-4090
卷号	16 期号:1 页码:105-129
摘要	We investigate the growth of the Nevanlinna characteristic of f(z+eta) for a fixed eta epsilon C in this paper. In particular, we obtain a precise asymptotic relation between T(r,f(z+eta)) and T(r,f), which is only true for finite order meromorphic functions. We have also obtained the proximity function and pointwise estimates of f(z+eta)/f(z) which is a discrete version of the classical logarithmic derivative estimates of f(z). We apply these results to give new growth estimates of meromorphic solutions to higher order linear difference equations. This also allows us to solve an old problem of Whittaker (Interpolatory Function Theory, Cambridge University Press, Cambridge, 1935) concerning a first order difference equation. We show by giving a number of examples that all of our results are best possible in certain senses. Finally, we give a direct proof of a result in Ablowitz, Halburd and Herbst (Nonlinearity 13:889-905, 2000) concerning integrable difference equations.
关键词	Poisson-Jensen formula meromorphic functions order of growth difference equations
DOI	10.1007/s11139-007-9101-1
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000256325600010
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5661
专题	系统科学研究所
通讯作者	Chiang, Yik-Man
作者单位	1.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chiang, Yik-Man,Feng, Shao-Ji. On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane[J]. RAMANUJAN JOURNAL,2008,16(1):105-129.
APA	Chiang, Yik-Man,&Feng, Shao-Ji.(2008).On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane.RAMANUJAN JOURNAL,16(1),105-129.
MLA	Chiang, Yik-Man,et al."On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane".RAMANUJAN JOURNAL 16.1(2008):105-129.