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Nevanlinna theory of the Askey-Wilson di...
Chiang, Yik-Man...

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Nevanlinna theory of the Askey-Wilson divided difference operator by Chiang, Yik-Man ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
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 $\mathbb{C}$. 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-Wilosn 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.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1502.02238
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