Year: 2025
Type: article
Abstract: Best uniform rational approximations of the odd and even Cauchy transforms are considered. The results obtained form a basis for finding the weak asymptotics of best uniform rational approximations of the odd extension of the function $x^{\alpha}$, $x\in[0,1]$, to $[-1,1]$ for all $alpha\in(0,+\infty)\setminus(2\mathbb N-1)$, which complements some results due to Vyacheslavov. The strong asymptotics of the best rational approximations of this function on $[0,1]$ and its even extension to $[-1,1]$ were found by Stahl. It follows from these results that for $alpha\in(0,+\infty)\setminus\mathbb N$ the best rational approximations of the even and odd extensions of the above function show the same weak asymptotic behaviour. Bibliography: 29 titles.
Source: Sbornik Mathematics
DOI: 10.4213/sm10116e
Author: Tatiana Sergeevna Mardvilko
Institution: Belarusian State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409492972