ISSN: 2310-757X
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http://elar.urfu.ru/handle/10995/93063| Title: | On An Extremal Problem for Polynomials with Fixed Mean Value |
| Authors: | Babenko, A. G. |
| Issue Date: | 2016 |
| Publisher: | N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences Ural Federal University named after the first President of Russia B.N. Yeltsin |
| Citation: | Babenko A. G. On An Extremal Problem for Polynomials with Fixed Mean Value / A. G. Babenko. — DOI 10.15826/umj.2016.1.001. — Text : electronic // Ural Mathematical Journal. — 2016. — Volume 2. — № 1. — P. 3-8. |
| Abstract: | Let T+n be the set of nonnegative trigonometric polynomials τn of degree n that are strictly positive at zero. For 0≤α≤2π/(n+2), we find the minimum of the mean value of polynomial (cosα−cosx)τn(x)/τn(0) over τn∈T+n on the period [−π,π). |
| Keywords: | TRIGONOMETRIC POLYNOMIALS EXTREMAL PROBLEM |
| URI: | http://elar.urfu.ru/handle/10995/93063 |
| Access: | Creative Commons Attribution License |
| License text: | https://creativecommons.org/licenses/by/4.0/ |
| ISSN: | 2414-3952 |
| DOI: | 10.15826/umj.2016.1.001 |
| Sponsorship: | The paper was originally published in a hard accessible collection of articles Approximation of Functionsby Polynomials and Splines (The Ural Scientific Center of the Academy of Sciences of the USSR, Sverdlovsk, 1985), p. 15-22 (in Russian). The author is grateful to Professor V.V. Arestov for the statement of the problem as well as to Doctor E.E. Berdysheva for the excellent translation of the paper into English. |
| Origin: | Ural Mathematical Journal. 2016. Volume 2. № 1 |
| Appears in Collections: | Ural Mathematical Journal |
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