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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 1992, Volume 1, Pages 50–70
(Mi timm448)
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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), (a≥0, n≥1) be the set of nonnegative trigonometric polynomials f(t)=∑nk=0akcoskt with a0=1, a1=a, ak≥0(k=2,…,n) The function
un(a)=inf{f(0)=n∑k=0ak:f∈C+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
Citation:
V. V. Arestov, “On extremal properties of the nonnegative trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 1, 1992, 50–70
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https://www.mathnet.ru/eng/timm448 https://www.mathnet.ru/eng/timm/v1/p50
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