Askey-Wilson均差算子的Nevanlinna理论
Nevanlinna theory of the Askey-Wilson divided difference operator
摘要：
本文对复平面$\mathbb{C}$中的有限对数级亚纯函数建立了一种基于Askey-Wilson均差算子的Nevanlinna理论.第二个主要定理，我们已经推导出允许我们定义一个Askey-Wilson型Nevanlinna不足，它给出了一个新的解释，人们应该把许多重要的无穷乘积所产生的研究基本超几何级数的零/极点稀缺。也就是说，它们的零点/极点在Nevanlinna理论的差异意义上确实是不足的。一个自然的推论是Askey-Wilosn型Picard定理的一个版本。我们还给出了一个替代和自包含的Askey-Wilson算子的核函数的特性。此外，我们还建立了Askey-Wilson意义下的唯一性定理。本文的结论是应用于差分方程推广的Askey-Wilson二阶均差方程。
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 $\mathbb{C}$. 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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