Geodesic
Remark on a Problem of Rational Approximation
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 446-448 
A. P. Starovoitov. Remark on a Problem of Rational Approximation. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 446-448. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a12/
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     title = {Remark on a {Problem} of {Rational} {Approximation}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We show that for any nonincreasing number sequence $\{a_n\}^{\infty}_{n=0}$ converging to zero, there exists a continuous $2\pi$-periodic function $g$ such that the sequence of its best uniform trigonometric rational approximations $\{R_n(g,C_{2\pi})\}^{\infty}_{n=0}$ and the sequence $\{a_n\}^{\infty}_{n=0}$ have the same order of decay.

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