Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 729-737
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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/
@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
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.
