INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE
The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci \(\pm 1\) of the derivative of an a...
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2020-12-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/283 |
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| _version_ | 1849251295551029248 |
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| author | Tatiana M. Nikiforova |
| author_facet | Tatiana M. Nikiforova |
| author_sort | Tatiana M. Nikiforova |
| collection | DOAJ |
| description | The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci \(\pm 1\) of the derivative of an algebraic polynomial with real coefficients normalized on the segment \([- 1,1]\). |
| format | Article |
| id | doaj-art-936f4dda7a4c42ffbe009608e011df44 |
| institution | Kabale University |
| issn | 2414-3952 |
| language | English |
| publishDate | 2020-12-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-936f4dda7a4c42ffbe009608e011df442025-08-20T03:56:59ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522020-12-016210.15826/umj.2020.2.009107INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSETatiana M. Nikiforova0Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620990; Ural Federal University, 19 Mira str., Ekaterinburg, 620002The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci \(\pm 1\) of the derivative of an algebraic polynomial with real coefficients normalized on the segment \([- 1,1]\).https://umjuran.ru/index.php/umj/article/view/283polynomial, chebyshev polynomials, ellipse, segment, derivative of a polynomial, uniform norm |
| spellingShingle | Tatiana M. Nikiforova INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE Ural Mathematical Journal polynomial, chebyshev polynomials, ellipse, segment, derivative of a polynomial, uniform norm |
| title | INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE |
| title_full | INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE |
| title_fullStr | INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE |
| title_full_unstemmed | INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE |
| title_short | INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE |
| title_sort | inequalities for algebraic polynomials on an ellipse |
| topic | polynomial, chebyshev polynomials, ellipse, segment, derivative of a polynomial, uniform norm |
| url | https://umjuran.ru/index.php/umj/article/view/283 |
| work_keys_str_mv | AT tatianamnikiforova inequalitiesforalgebraicpolynomialsonanellipse |