关于具有预设极点的有理函数的不等式
Inequalities Concerning Rational Functions With Prescribed Poles
AI总结：
本文研究了具有预设极点的有理函数不等式，推导了新的结果并推广了已知的多项式不等式。
摘要：
令$\Re_n$为所有形如$r(z) = p(z)/w(z)$的有理函数的集合，其中$p(z)$是一个次数不超过$n$的多项式，而$w(z) = \prod_{j=1}^{n}(z-a_j)$，其中$|a_j|>1$对于$1\leq j\leq n$。本文针对具有固定极点和受限零点的有理函数建立了一些结果。所得结果不仅对已知的有理函数不等式进行了推广和修正，还进一步对某些多项式不等式进行了推广和修正。
英文摘要：
Let $\Re_n$ be the set of all rational functions of the type $r(z) = p(z)/w(z),$ where $p(z)$ is a polynomial of degree at most $n$ and $w(z) = \prod_{j=1}^{n}(z-a_j)$, $|a_j|>1$ for $1\leq j\leq n$. In this paper, we set up some results for rational functions with fixed poles and restricted zeros. The obtained results bring forth generalizations and refinements of some known inequalities for rational functions and in turn produce generalizations and refinements of some polynomial inequalities as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
