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Matematicheskie Zametki, 1977, Volume 22, Issue 3, Pages 371–374 (Mi mzm8057)  

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

Some extremal properties of positive trigonometric polynomials

V. P. Kondrat'ev

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR
Full-text PDF (278 kB) Citations (3)
Abstract: For n=8 an upper bound is given for the functional
Vn=inftna1+a2++an(aqa0)2,
which is defined on the class of even, nonnegative, trigonometric polynomials tn(φ)=nk=0akcoskφ, such that ak0 (k=0,\dots,n), a_1>a_0:V_8\le34,\!54461566.
Received: 20.08.1976
English version:
Mathematical Notes, 1977, Volume 22, Issue 3, Pages 696–698
DOI: https://doi.org/10.1007/BF02412497
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: V. P. Kondrat'ev, “Some extremal properties of positive trigonometric polynomials”, Mat. Zametki, 22:3 (1977), 371–374; Math. Notes, 22:3 (1977), 696–698
Citation in format AMSBIB
\Bibitem{Kon77}
\by V.~P.~Kondrat'ev
\paper Some extremal properties of positive trigonometric polynomials
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 3
\pages 371--374
\mathnet{http://mi.mathnet.ru/mzm8057}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=485725}
\zmath{https://zbmath.org/?q=an:0361.10034}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 3
\pages 696--698
\crossref{https://doi.org/10.1007/BF02412497}
Linking options:
  • https://www.mathnet.ru/eng/mzm8057
  • https://www.mathnet.ru/eng/mzm/v22/i3/p371
  • This publication is cited in the following 3 articles:
    1. Nicol Leong, Michael J. Mossinghoff, “A note on trigonometric polynomials for lower bounds of \zeta(s)”, Funct. Approx. Comment. Math., -1:-1 (2025)  crossref
    2. M. R. Gabdullin, S. V. Konyagin, “O rabotakh S. B. Stechkina po teorii chisel”, Chebyshevskii sb., 21:4 (2020), 9–18  mathnet  crossref
    3. Michael J. Mossinghoff, Timothy S. Trudgian, “Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function”, Journal of Number Theory, 157 (2015), 329  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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