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On the Nevanlinna characteristic of f(z+eta) and difference equations in the complex plane
文献类型：期刊论文
| 作者 | Chiang, Yik-Man1; Feng, Shao-Ji2
|
| 刊名 | RAMANUJAN JOURNAL
 |
| 出版日期 | 2008-05-01 |
| 卷号 | 16期号:1页码:105-129 |
| 关键词 | Poisson-Jensen formula meromorphic functions order of growth difference equations |
| ISSN号 | 1382-4090 |
| DOI | 10.1007/s11139-007-9101-1 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000256325600010 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5660]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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