On the extremal problem about the minimum of the free term of a~nonnegative trigonometric polynomial
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 105-121
Voir la notice de l'article provenant de la source Math-Net.Ru
A new extremal problem is solved about the minimum of the free term of a nonnegative even trigonometric polynomial with the following conditions on its coefficients: all coefficients except for the free term are greater than or equal to 1 and the sum of all coefficients except for the free term is equal to a specified value. As a result, Fejér's known result is improved.
Keywords:
extremal problem, nonnegative trigonometric polynomial.
@article{TIMM_2011_17_3_a12,
author = {A. S. Belov},
title = {On the extremal problem about the minimum of the free term of a~nonnegative trigonometric polynomial},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {105--121},
publisher = {mathdoc},
volume = {17},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a12/}
}
TY - JOUR AU - A. S. Belov TI - On the extremal problem about the minimum of the free term of a~nonnegative trigonometric polynomial JO - Trudy Instituta matematiki i mehaniki PY - 2011 SP - 105 EP - 121 VL - 17 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a12/ LA - ru ID - TIMM_2011_17_3_a12 ER -
%0 Journal Article %A A. S. Belov %T On the extremal problem about the minimum of the free term of a~nonnegative trigonometric polynomial %J Trudy Instituta matematiki i mehaniki %D 2011 %P 105-121 %V 17 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a12/ %G ru %F TIMM_2011_17_3_a12
A. S. Belov. On the extremal problem about the minimum of the free term of a~nonnegative trigonometric polynomial. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 105-121. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a12/