论文标题
Zolotarev的第五和第六个问题
Zolotarev's fifth and sixth problems
论文作者
论文摘要
在1877年有影响力的论文中，Zolotarev询问并回答了有关多项式和理性近似的四个问题。 We ask and answer two questions: what are the best rational approximants $r$ and $s$ to $\sqrt{z}$ and $\mbox{sign}(z)$ on the unit circle (excluding certain arcs near the discontinuities), with the property that $|r(z)|=|s(z)|=1$ for $|z|=1$?我们表明，解决这些问题的解决方案与Zolotarev的第三和第四个问题有关。
In an influential 1877 paper, Zolotarev asked and answered four questions about polynomial and rational approximation. We ask and answer two questions: what are the best rational approximants $r$ and $s$ to $\sqrt{z}$ and $\mbox{sign}(z)$ on the unit circle (excluding certain arcs near the discontinuities), with the property that $|r(z)|=|s(z)|=1$ for $|z|=1$? We show that the solutions to these problems are related to Zolotarev's third and fourth problems in a nontrivial manner.
