Abstract
The following problem, bound up with Weierstrass's classical approximation theorem, is solved definitively: to determine the sequence of positive numbersM k such that, for anyf(z)εc[0,1] and ∀ > 0 there exists the polynomial\(P\left( z \right) = \sum\nolimits_0^n {\lambda _k z^k } \) that ∥f−P∥<ε and ∣λ k ∣<εM k ,k=1, ...,n.
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Translated from Matematicheskii Zametki, Vol. 22, No. 2, pp. 269–276, August, 1977.
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Muradyan, O.A., Khavinson, S.Y. Absolute values of the coefficients of the polynomials in Weierstrass's approximation theorem. Mathematical Notes of the Academy of Sciences of the USSR 22, 641–645 (1977). https://doi.org/10.1007/BF01780974
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DOI: https://doi.org/10.1007/BF01780974