Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Gawlik, Evan S., Nakatsukasa, Yuji
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3107782097