Sign changes in rational Lw1-approximation

• Date: 2006
• Main Authors: Blatt, H. P., Grothmann, R., Kovacheva, R. K., Блат, Х.П., Гросман, Р., Ковачева, Р. К.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3452
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $f \in L_{1}^{w}[-1, 1]$, let $r_{n, m}(f)$ be a best rational $L_{1}^{w}$-approximation for $f$ with respect to real rational functions of degree at most n in the numerator and of degree at most m in the denominator, let $m = m(n)$, and let $\lim_{n\rightarrow \infty}(n - m(n)) = \infty$. The...