Geodesic
On an extremal problem on the minimum of a trigonometric polynomial
Izvestiya. Mathematics, Tome 43 (1994) no. 3, pp. 593-606 Cet article a éte moissonné depuis la source Math-Net.Ru

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The exact value of the quantity $$ M(n)=\min\biggl\{-\min_x\sum_{k=1}^na_k\cos(kx)\colon a_1\geqslant 1,\dots ,a_n\geqslant 1\biggr\} $$ is found for any positive integer $n$. It is proved that an extremal trigonometric polynomial on which this minimum is attained is unique. Some properties of these extremal polynomials are studied. 
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A. S. Belov. On an extremal problem on the minimum of a trigonometric polynomial. Izvestiya. Mathematics, Tome 43 (1994) no. 3, pp. 593-606. http://geodesic.mathdoc.fr/item/IM2_1994_43_3_a10/

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