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On an extremal problem for polynomials with fixed mean value
Alexander G. Babenkoab a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg, Russia
Аннотация:
Let $T_n^+$ be the set of nonnegative trigonometric polynomials $\tau_n$ of degree $n$ that are strictly positive at zero. For $0\le\alpha\le2\pi/(n+2),$ we find the minimum of the mean value of polynomial $(\cos\alpha-\cos{x})\tau_n(x)/\tau_n(0)$ over $\tau_n\in{T_n^+}$ on the period $[-\pi,\pi).$
The paper was originally published in a hard accessible collection of articles Approximation of Functions by Polynomials and Splines (The Ural Scientific Center of the Academy of Sciences of the USSR, Sverdlovsk,
1985), p. 15–22 (in Russian).
Ключевые слова:
Trigonometric polynomials, Extremal problem.
Образец цитирования:
Alexander G. Babenko, “On an extremal problem for polynomials with fixed mean value”, Ural Math. J., 2:1 (2016), 3–8
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj10 https://www.mathnet.ru/rus/umj/v2/i1/p3
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Страница аннотации: | 218 | PDF полного текста: | 78 | Список литературы: | 46 |
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