Geodesic
On the problem of the~description of sequences of best rational trigonometric approximations
Sbornik. Mathematics, Tome 191 (2000) no. 6, pp. 927-936

Voir la notice de l'article provenant de la source Math-Net.Ru

For a fixed sequence $\{a_n\}^\infty_{n=0}$ of non-negative real numbers strictly decreasing to zero a continuous $2\pi$-periodic function $f$ is constructed such that $R^T_n(f)=a_n$, $n=0,1,2,\dots$, where the $R^T_n(f)$ are the best approximations of $f$ in the uniform norm by rational trigonometric functions of degree at most $n$. 
@article{SM_2000_191_6_a6,
     author = {A. P. Starovoitov},
     title = {On the problem of the~description of sequences of best rational trigonometric approximations},
     journal = {Sbornik. Mathematics},
     pages = {927--936},
     publisher = {mathdoc},
     volume = {191},
     number = {6},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_6_a6/}
}
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A. P. Starovoitov. On the problem of the~description of sequences of best rational trigonometric approximations. Sbornik. Mathematics, Tome 191 (2000) no. 6, pp. 927-936. http://geodesic.mathdoc.fr/item/SM_2000_191_6_a6/