Nevanlinna theory of the Askey-Wilson divided difference operator

doi:10.1016/j.aim.2018.02.006

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	Nevanlinna theory of the Askey-Wilson divided difference operator
	Chiang, Yik-Man 1; Feng, Shaoji2
	2018-04-30
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	329 页码:217-272
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.
关键词	Nevanlinna theory Askey-Wilson operator Deficiency Difference equations
DOI	10.1016/j.aim.2018.02.006
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000431089100007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30209
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.