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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 1992, Volume 1, Pages 50–70 (Mi timm448)  

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

Function theory, approximation theory

On extremal properties of the nonnegative trigonometric polynomials

V. V. Arestov
Abstract: Let C+n(a), (a0, n1) be the set of nonnegative trigonometric polynomials f(t)=nk=0akcoskt with a0=1, a1=a, ak0(k=2,,n) The function
un(a)=inf{f(0)=nk=0ak:fC+n(a)}
on the segment [0,A(n)], A(n)=2cosπn+2, has been studied. Values of the un(a) for the close to A(n) arguments a have been obtained. The results given in the present article have been applied to the problem of Ch.-J. Vallé Poussin and E. Landau that cropped up in the course of their investigation on the prime number theory.
Received: 15.11.1990
Bibliographic databases:
Document Type: Article
UDC: 517.518.86
MSC: 26D05
Language: Russian
Citation: V. V. Arestov, “On extremal properties of the nonnegative trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 1, 1992, 50–70
Citation in format AMSBIB
\Bibitem{Are92}
\by V.~V.~Arestov
\paper On extremal properties of the nonnegative trigonometric polynomials
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 1992
\vol 1
\pages 50--70
\mathnet{http://mi.mathnet.ru/timm448}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1299783}
\zmath{https://zbmath.org/?q=an:0815.42002}
\elib{https://elibrary.ru/item.asp?id=12138810}
Linking options:
  • https://www.mathnet.ru/eng/timm448
  • https://www.mathnet.ru/eng/timm/v1/p50
  • This publication is cited in the following 6 articles:
    1. V. I. Danchenko, D. G. Chkalova, “Bernstein-type estimates for the derivatives of trigonometric polynomials”, Probl. anal. Issues Anal., 10(28):3 (2021), 31–40  mathnet  crossref
    2. D. G. Vasilchenkova, V. I. Danchenko, “Extraction of harmonics from trigonometric polynomials by phase-amplitude operators”, St. Petersburg Math. J., 32:2 (2021), 215–232  mathnet  crossref  isi  elib
    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  mathscinet  isi  elib
    4. M. I. Gusev, “Optimal inputs in guaranteed identification problems”, Proc. Inst. Math. Mech., 2005no. , suppl. 1, S95–S106  mathnet  mathscinet  zmath
    5. Dimitrov D.K., Merlo C.A., “Nonnegative trigonometric polynomials”, Constructive Approximation, 18:1 (2002), 117–143  crossref  mathscinet  zmath  isi
    6. A. G. Babenko, “An exact Jackson–Stechkin inequality for L2-approximation on the interval with the Jacobi weight and on projective spaces”, Izv. Math., 62:6 (1998), 1095–1119  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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