Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 371-374
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V. P. Kondrat'ev. Some extremal properties of positive trigonometric polynomials. Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 371-374. http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a5/
@article{MZM_1977_22_3_a5,
author = {V. P. Kondrat'ev},
title = {Some extremal properties of positive trigonometric polynomials},
journal = {Matemati\v{c}eskie zametki},
pages = {371--374},
year = {1977},
volume = {22},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a5/}
}
TY - JOUR
AU - V. P. Kondrat'ev
TI - Some extremal properties of positive trigonometric polynomials
JO - Matematičeskie zametki
PY - 1977
SP - 371
EP - 374
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a5/
LA - ru
ID - MZM_1977_22_3_a5
ER -
%0 Journal Article
%A V. P. Kondrat'ev
%T Some extremal properties of positive trigonometric polynomials
%J Matematičeskie zametki
%D 1977
%P 371-374
%V 22
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a5/
%G ru
%F MZM_1977_22_3_a5
For $n=8$ an upper bound is given for the functional $$ V_n=\inf_{t_n}\frac{a_1+a_2+\dots+a_n}{(\sqrt{a_q}-\sqrt{a_0})^2}, $$ which is defined on the class of even, nonnegative, trigonometric polynomials $t_n(\varphi)=\sum_{k=0}^na_k\cos k\varphi$, such that $a_k\ge0$ ($k=0,\dots,n$), $a_1>a_0:V_8\le34,\!54461566$.
