Sign changes in rational Lw1-approximation
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...
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| Дата: | 2006 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2006
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3452 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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