Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 269-276
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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 $|\lambda_k|\varepsilon M_k$, $k=1,\dots,n$.
@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},
publisher = {mathdoc},
volume = {22},
number = {2},
year = {1977},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a10/ %G ru %F MZM_1977_22_2_a10
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/