POLYNOMIALS LEAST DEVIATING FROM ZERO IN LP(-1; 1), 0 ≤ P ≤∞, WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
POLYNOMIALS LEAST DEVIATING FROM ZERO IN LP(-1; 1), 0 ≤ P ≤∞, WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS
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| Автор |
Rokina, A. E.
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| Тематика |
ALGEBRAIC POLYNOMIALS
CHEBYSHEV POLYNOMIALS CONSTRAINTS ON THE ROOTS OF A POLYNOMIAL |
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| Описание |
We study Chebyshev's problem on polynomials that deviate least from zero with respect to Lp-means on the interval [-1;1] with a constraint on the location of roots of polynomials. More precisely, we consider the problem on the set Pn(DR) of polynomials of degree n that have unit leading coefficient and do not vanish in an open disk of radius R ≥ 1. An exact solution is obtained for the geometric mean (for p=0) for all R ≥ 1, and for 0 < p < ∞ for all R ≥ 1 in the case of polynomials of even degree. For 0 < p < ∞ and R ≥ 1, we obtain two-sided estimates of the value of the least deviation.
This work was supported by the Russian Science Foundation, project no. 22-21-00526, https://rscf.ru/project/22-21-00526/ . |
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| Дата |
2024-02-14T05:20:42Z
2024-02-14T05:20:42Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Rokina A. E. POLYNOMIALS LEAST DEVIATING FROM ZERO IN LP(-1; 1), 0 ≤ P ≤∞, WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS / A. E. Rokina. — Text : electronic // Ural Mathematical Journal. — 2023. — Volume 9. — № 2. — P. 157-164.
2414-3952 https://umjuran.ru/index.php/umj/article/view/674 http://elar.urfu.ru/handle/10995/129425 59690665 10.15826/umj.2023.2.013 |
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| Язык |
en
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| Связанные ресурсы |
Ural Mathematical Journal. 2023. Volume 9. № 2
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| Права |
Creative Commons Attribution License
https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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