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. © 2023, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Russian Science Foundation, RSF: 22-21-00526 1This work was supported by the Russian Science Foundation, https://rscf.ru/project/22-21-00526/ . 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 |
2024-04-05T16:38:45Z
2024-04-05T16:38:45Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Rokina, A 2023, 'POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS', Ural Mathematical Journal, Том. 9, № 2, стр. 157-164. https://doi.org/10.15826/umj.2023.2.013
Rokina, A. (2023). POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS. Ural Mathematical Journal, 9(2), 157-164. https://doi.org/10.15826/umj.2023.2.013 2414-3952 Final All Open Access, Gold https://www.scopus.com/inward/record.uri?eid=2-s2.0-85180901198&doi=10.15826%2fumj.2023.2.013&partnerID=40&md5=150094d8181b361b9884da7a28c12897 https://umjuran.ru/index.php/umj/article/download/674/pdf http://elar.urfu.ru/handle/10995/131091 59690665 10.15826/umj.2023.2.013 85180901198 |
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| Язык |
en
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| Связанные ресурсы |
info:eu-repo/grantAgreement/RSF//22-21-00526
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Krasovskii Institute of Mathematics and Mechanics
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| Источник |
Ural Mathematical Journal
Ural Mathematical Journal |
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