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Nevanlinna theory of the Askey-Wilson divided difference operator
Chiang, Yik-Man1; Feng, Shaoji2
2018-04-30
Source PublicationADVANCES IN MATHEMATICS
ISSN0001-8708
Volume329Pages:217-272
AbstractThis 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.
KeywordNevanlinna theory Askey-Wilson operator Deficiency Difference equations
DOI10.1016/j.aim.2018.02.006
Language英语
Funding ProjectResearch 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000431089100007
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30209
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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