ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE
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 \([...
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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
2016-07-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/39 |
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| author | Alexander G. Babenko |
| author_facet | Alexander G. Babenko |
| author_sort | Alexander G. Babenko |
| collection | DOAJ |
| description | 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 \([-\pi,\pi).\) |
| format | Article |
| id | doaj-art-da21b2d404ec49469b6461ce4bde2475 |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2016-07-01 |
| 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-da21b2d404ec49469b6461ce4bde24752025-08-20T02:51:20ZengUral 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 Journal2414-39522016-07-012110.15826/umj.2016.1.00110ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUEAlexander G. Babenko0Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences; Institute of Mathematics and Computer Science of the Ural Federal University, EkaterinburgLet \(T_n^+\) 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 \([-\pi,\pi).\)https://umjuran.ru/index.php/umj/article/view/39Trigonometric polynomials, Extremal problem |
| spellingShingle | Alexander G. Babenko ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE Ural Mathematical Journal Trigonometric polynomials, Extremal problem |
| title | ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE |
| title_full | ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE |
| title_fullStr | ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE |
| title_full_unstemmed | ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE |
| title_short | ON AN EXTREMAL PROBLEM FOR POLYNOMIALS WITH FIXED MEAN VALUE |
| title_sort | on an extremal problem for polynomials with fixed mean value |
| topic | Trigonometric polynomials, Extremal problem |
| url | https://umjuran.ru/index.php/umj/article/view/39 |
| work_keys_str_mv | AT alexandergbabenko onanextremalproblemforpolynomialswithfixedmeanvalue |