AI 中文总结
该研究推导了一类特定权重的加权移位算子的数值半径界，给出了确定其数值半径的整函数方法，推广了已有相关研究成果。
AI 中文摘要
本文推导了权重为(1,sq,q²,tq³,q⁴,sq⁵,q⁶,tq⁷,…)（其中s,t>0且0<q<1）的加权移位算子T的数值半径的若干界；还给出了整函数F_T(z)，方程F_T(z)=0的最小正根的倒数即为T的数值半径，这些结果推广了文献[chakraborty2025numerical]中讨论的加权移位算子数值半径的若干已知结果。
英文摘要
In this paper, we derive some bounds on numerical radius of the weighted shift operator $T$ with weights $(1,sq,q^2,tq^3,q^4,sq^5,q^6,tq^7,\ldots)$ where $s,t >0$ and $0<q<1$. Furthermore, we provide an entire function $F_T(z)$. The reciprocal of the minimal positive root of $F_T(z)=0$ gives the numerical radius of $T$. These results generalize several previously known results on the numerical radius of weighted shift operators discussed in \cite{chakraborty2025numerical}.
