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Mat. Zametki, 1970, Volume 7, Issue 4, Pages 411–422 (Mi mz9524)  

This article is cited in 2 scientific papers (total in 3 papers)

Some extremal properties of positive trigonometric polynomials

S. B. Stechkin

V. A. Steklov Mathematical Institute, Academy of Sciences of the USSR

Abstract: A class $P_n$ of even positive trigonometric polynomials $t_n(\varphi)=a_0+a_1\cos\varphi+…+a_n\cos n\varphi$, satisfying the conditions: $a_k\geqslant0$ ($k=0,1,…,n$), $a_0<a_1$ is considered. The behavior of the sequence of functionals
$$ V_n=\inf_{t_n\in P_n}\frac{t_n(0)-a_0}{(\sqrt{a_1}-\sqrt{a_0})^2}, $$
is studied; two-sided estimations are given for $V_n$ and $V_\infty=\lim\limits_{n\to\infty}V_n$.

Full text: PDF file (914 kB)

English version:
Mathematical Notes, 1970, 7:4, 248–255

Bibliographic databases:

UDC: 517.5
Received: 20.11.1969

Citation: S. B. Stechkin, “Some extremal properties of positive trigonometric polynomials”, Mat. Zametki, 7:4 (1970), 411–422; Math. Notes, 7:4 (1970), 248–255

Citation in format AMSBIB
\Bibitem{Ste70}
\by S.~B.~Stechkin
\paper Some extremal properties of positive trigonometric polynomials
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 4
\pages 411--422
\mathnet{http://mi.mathnet.ru/mz9524}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=263755}
\zmath{https://zbmath.org/?q=an:0219.10049}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 4
\pages 248--255
\crossref{https://doi.org/10.1007/BF01151697}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Besov, V. M. Buchstaber, A. G. Vitushkin, A. A. Gonchar, S. V. Konyagin, L. D. Kudryavtsev, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, A. Yu. Popov, V. A. Sadovnichii, A. F. Sidorov, Yu. N. Subbotin, S. A. Telyakovskii, P. L. Ul'yanov, N. I. Chernykh, “Sergei Borisovich Stechkin (obituary)”, Russian Math. Surveys, 51:6 (1996), 1007–1014  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. D. G. Vasilchenkova, V. I. Danchenko, “Vydelenie garmonik iz trigonometricheskikh mnogochlenov amplitudno-fazovymi operatorami”, Algebra i analiz, 32:2 (2020), 21–44  mathnet
    3. D. G. Vasilchenkova, V. I. Danchenko, “Extraction of Several Harmonics from Trigonometric Polynomials. Fejér-Type Inequalities”, Proc. Steklov Inst. Math., 308 (2020), 92–106  mathnet  crossref  crossref  isi  elib
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