Geodesic
On the asymptotic solution of one extremal problem related to nonnegative trigonometric polynomials
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 27-67 
A. S. Belov. On the asymptotic solution of one extremal problem related to nonnegative trigonometric polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 5, pp. 27-67. http://geodesic.mathdoc.fr/item/FPM_2013_18_5_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For every real number $\gamma\ge1$ we denote by $K^\downarrow(\gamma)$ the least possible value of the constant term of an even nonnegative trigonometric polynomial with monotone coefficients such that all its coefficients, save for the constant term, are not less than $1$ and the sum of these coefficients equals $\gamma$. In this paper, the asymptotic estimate of $K^\downarrow(\gamma)$ is found and some extremal problems on the minimum of the constant term of an even nonnegative trigonometric polynomial are studied.

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