论文标题
基于Askey-Wilson操作员的多项式系列的Wiman-Valiron理论
Wiman-Valiron theory for a polynomial series based on the Askey-Wilson operator
论文作者
论文摘要
我们建立了一个基于Askey-Wilson操作员$ \ MATHCAL {D} _Q $的多项式系列的Wiman-Valiron理论，其中$ q \ in（0,1）$。对于整个函数$ f $的日志订单小于$ 2 $，该理论包括（i）估计，该估计表明，$ f $在其Askey-Wilson系列扩展的最大术语附近的多项式上的行为，以及（ii）$ \ natercal {d} _q^n f $相比的估计值。然后，我们将该理论应用于研究整个解决方案的增长到涉及Askey-Wilson操作员的差异方程。
We establish a Wiman-Valiron theory of a polynomial series based on the Askey-Wilson operator $\mathcal{D}_q$, where $q\in(0,1)$. For an entire function $f$ of log-order smaller than $2$, this theory includes (i) an estimate which shows that $f$ behaves locally like a polynomial consisting of the terms near the maximal term of its Askey-Wilson series expansion, and (ii) an estimate of $\mathcal{D}_q^n f$ compared to $f$. We then apply this theory in studying the growth of entire solutions to difference equations involving the Askey-Wilson operator.
