Sign changes in rational <i>L<sub>w</sub></i><sup>1</sup>-approximation

  • H. P. Blatt
  • R. Grothmann
  • R. K. Kovacheva

Abstract

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 $\lim_{n\rightarrow \infty}(n - m(n)) = \infty$. Then we show that the counting measures of certain subsets of sign changes of $f - r_{n,m}(f)$ converge weakly to the equilibrium measure on $[-1, 1]$ as $n\rightarrow \infty$. Moreover, we prove discrepancy estimates between these counting measures and the equilibrium measure.
Published
25.02.2006
How to Cite
Blatt, H. P., R. Grothmann, and R. K. Kovacheva. “Sign Changes in Rational <i>L<sub>w</sub></i><sup>1</Sup&gt;-Approximation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 2, Feb. 2006, pp. 283–287, http://umj.imath.kiev.ua/index.php/umj/article/view/3452.
Section
Short communications