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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 92–111 (Mi timm192)  

This article is cited in 6 scientific papers (total in 6 papers)

Some extremal problems for periodic functions with conditions on their values and Fourier coefficients

V. I. Ivanov, D. V. Gorbachev, Yu. D. Rudomazina


Abstract: A solution of the discrete variant of the Fejér problem on the greatest value, at zero, of an even nonnegative trigonometric polynomial with fixed average is given. As a corollary, for all rational $h$, $0<h\le1/2$, the greatest averages are obtained for continuous 1-periodic even functions, with nonnegative Fourier coefficients and a fixed value at zero, equal to zero on the segment $[h,1-h]$ (the Turán problem) or nonpositive on this segment (the Delsarte problem). Similar problems are also solved in the discrete case. In addition, in one case, a solution of the extremal Montgomery problem for nonnegative trigonometric polynomials is given.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S139–S159

Bibliographic databases:
UDC: 517.977
Received: 10.09.2004

Citation: V. I. Ivanov, D. V. Gorbachev, Yu. D. Rudomazina, “Some extremal problems for periodic functions with conditions on their values and Fourier coefficients”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 92–111; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S139–S159

Citation in format AMSBIB
\Bibitem{IvaGorRud05}
\by V.~I.~Ivanov, D.~V.~Gorbachev, Yu.~D.~Rudomazina
\paper Some extremal problems for periodic functions with conditions on their values and Fourier coefficients
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 92--111
\mathnet{http://mi.mathnet.ru/timm192}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200226}
\zmath{https://zbmath.org/?q=an:1137.42001}
\elib{http://elibrary.ru/item.asp?id=12040706}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S139--S159


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. I. Ivanov, “On the Turán and Delsarte problems for periodic positive definite functions”, Math. Notes, 80:6 (2006), 875–880  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Berdysheva E.E., Berens H., “About a Turan problem for l-1 radial, positive definite functions, II”, Journal of Approximation Theory, 160:1–2 (2009), 71–88  crossref  mathscinet  zmath  isi  scopus
    3. D. V. Gorbachev, V. I. Ivanov, “Nekotorye ekstremalnye zadachi dlya preobrazovaniya Fure po sobstvennym funktsiyam operatora Shturma–Liuvillya”, Chebyshevskii sb., 18:2 (2017), 34–53  mathnet  crossref  elib
    4. D. V. Gorbachev, V. I. Ivanov, E. P. Ofitserov, O. I. Smirnov, “Nekotorye ekstremalnye zadachi garmonicheskogo analiza i teorii priblizhenii”, Chebyshevskii sb., 18:4 (2017), 140–167  mathnet  crossref
    5. Gorbachev D.V., Tikhonov S.Yu., “Wiener'S Problem For Positive Definite Functions”, Math. Z., 289:3-4 (2018), 859–874  crossref  mathscinet  zmath  isi  scopus
    6. D. V. Gorbachev, V. I. Ivanov, “Turán, Fejér and Bohman extremal problems for the multivariate Fourier transform in terms of the eigenfunctions of a Sturm-Liouville problem”, Sb. Math., 210:6 (2019), 809–835  mathnet  crossref  crossref  adsnasa  isi  elib
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