Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 269-276
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O. A. Muradyan; S. Ya. Khavinson. Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 269-276. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a10/
@article{MZM_1977_22_2_a10,
author = {O. A. Muradyan and S. Ya. Khavinson},
title = {Absolute values of the coefficients of the polynomials in {Weierstrass's} approximation theorem},
journal = {Matemati\v{c}eskie zametki},
pages = {269--276},
year = {1977},
volume = {22},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a10/}
}
TY - JOUR
AU - O. A. Muradyan
AU - S. Ya. Khavinson
TI - Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem
JO - Matematičeskie zametki
PY - 1977
SP - 269
EP - 276
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a10/
LA - ru
ID - MZM_1977_22_2_a10
ER -
%0 Journal Article
%A O. A. Muradyan
%A S. Ya. Khavinson
%T Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem
%J Matematičeskie zametki
%D 1977
%P 269-276
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a10/
%G ru
%F MZM_1977_22_2_a10
The following problem, bound up with Weierstrass's classical approximation theorem, is solved definitively: to determine the sequence of positive numbers $\{M_k\}$ such that, for any $f(z)\in C[0,1]$ and $\forall\,\varepsilon>0$ there exists the polynomial $P(z)=\sum_0^n\lambda_kz^k$ that $\|f-P\|<\varepsilon$ and $|\lambda_k|<\varepsilon M_k$, $k=1,\dots,n$.
