On uniqueness of the polynomial of best approximation of the function $\cos kx$ by trigonometric polynomials in the $L$ metric
Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 729-737
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In this paper we clarify a problem concerning uniqueness of the polynomial which best approximates $\cos kx$ in the $L$ metric with respect to a trigonometric system of order $n$ in which $\cos kx$ is absent. We prove uniqueness in the case $n=(2l +1)k$. In the remaining cases there is no uniqueness. An analogous problem in the $C$ metric is solved and the relationship between $n$ and $k$ in the case of uniqueness ia distinguished from the conditions in the $L$ metric.
@article{MZM_1974_15_5_a8,
author = {V. N. Temlyakov},
title = {On uniqueness of the polynomial of best approximation of the function $\cos kx$ by trigonometric polynomials in the $L$ metric},
journal = {Matemati\v{c}eskie zametki},
pages = {729--737},
year = {1974},
volume = {15},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a8/}
}
TY - JOUR AU - V. N. Temlyakov TI - On uniqueness of the polynomial of best approximation of the function $\cos kx$ by trigonometric polynomials in the $L$ metric JO - Matematičeskie zametki PY - 1974 SP - 729 EP - 737 VL - 15 IS - 5 UR - http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a8/ LA - ru ID - MZM_1974_15_5_a8 ER -
%0 Journal Article %A V. N. Temlyakov %T On uniqueness of the polynomial of best approximation of the function $\cos kx$ by trigonometric polynomials in the $L$ metric %J Matematičeskie zametki %D 1974 %P 729-737 %V 15 %N 5 %U http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a8/ %G ru %F MZM_1974_15_5_a8
V. N. Temlyakov. On uniqueness of the polynomial of best approximation of the function $\cos kx$ by trigonometric polynomials in the $L$ metric. Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 729-737. http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a8/