Nevanlinna theory of the Askey-Wilson divided difference operator
文献类型：期刊论文
| 作者 | Chiang, Yik-Man1; Feng, Shaoji2
|
| 刊名 | ADVANCES IN MATHEMATICS
 |
| 出版日期 | 2018-04-30 |
| 卷号 | 329页码:217-272 |
| 关键词 | Nevanlinna theory Askey-Wilson operator Deficiency Difference equations |
| ISSN号 | 0001-8708 |
| DOI | 10.1016/j.aim.2018.02.006 |
| 英文摘要 | This paper establishes a version of Nevanlinna theory based on Askey-Wilson divided difference operator for meromorphic functions of finite logarithmic order in the complex plane C. A second main theorem that we have derived allows us to define an Askey-Wilson type Nevanlinna deficiency which gives a new interpretation that one should regard many important infinite products arising from the study of basic hypergeometric series as zero/pole-scarce. That is, their zeros/poles are indeed deficient in the sense of difference Nevanlinna theory. A natural consequence is a version of Askey-Wilson type Picard theorem. We also give an alternative and self-contained characterisation of the kernel functions of the Askey-Wilson operator. In addition we have established a version of unicity theorem in the sense of Askey-Wilson. This paper concludes with an application to difference equations generalising the Askey-Wilson second-order divided difference equation. (C) 2018 Elsevier Inc. All rights reserved. |
| 资助项目 | Research Grants Council of the Hong Kong Special Administrative Region, China[600806] ; Research Grants Council of the Hong Kong Special Administrative Region, China[600609] ; Research Grants Council of the Hong Kong Special Administrative Region, China[16306315] ; National Natural Science Foundation of China[11271352] ; HKUST PDF Matching Fund |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000431089100007 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/30208]  |
| 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, Shaoji. Nevanlinna theory of the Askey-Wilson divided difference operator[J]. ADVANCES IN MATHEMATICS,2018,329:217-272. |
| APA | Chiang, Yik-Man,&Feng, Shaoji.(2018).Nevanlinna theory of the Askey-Wilson divided difference operator.ADVANCES IN MATHEMATICS,329,217-272. |
| MLA | Chiang, Yik-Man,et al."Nevanlinna theory of the Askey-Wilson divided difference operator".ADVANCES IN MATHEMATICS 329(2018):217-272. |
入库方式： OAI收割
来源：数学与系统科学研究院
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