Geodesic
Some extremal properties of positive trigonometric polynomials
Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 411-422

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A class $P_n$ of even positive trigonometric polynomials $t_n(\varphi)=a_0+a_1\cos\varphi+\dots+a_n\cos n\varphi$, satisfying the conditions: $a_k\geqslant0$ ($k=0,1,\dots,n$), $a_0$ is considered. The behavior of the sequence of functionals $$ V_n=\inf_{t_n\in P_n}\frac{t_n(0)-a_0}{(\sqrt{a_1}-\sqrt{a_0})^2}, $$ is studied; two-sided estimations are given for $V_n$ and $V_\infty=\lim\limits_{n\to\infty}V_n$. 
@article{MZM_1970_7_4_a5,
     author = {S. B. Stechkin},
     title = {Some extremal properties of positive trigonometric polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {411--422},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a5/}
}
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S. B. Stechkin. Some extremal properties of positive trigonometric polynomials. Matematičeskie zametki, Tome 7 (1970) no. 4, pp. 411-422. http://geodesic.mathdoc.fr/item/MZM_1970_7_4_a5/