Geodesic
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 $|\lambda_k|\varepsilon M_k$, $k=1,\dots,n$. 
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     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/}
}
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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/