2017
Том 69
№ 5

All Issues

Sign changes in rational Lw1-approximation

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

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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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 2, pp 318-323.

Citation Example: Blatt H. P., Grothmann R., Kovacheva R. K. Sign changes in rational Lw1-approximation // Ukr. Mat. Zh. - 2006. - 58, № 2. - pp. 283–287.

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