Geodesic
Piecewise polynomial approximation
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 129-134.

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For best piecewise polynomial approximation $\mathscr{E}_n=\mathscr{E}_n(f;[0, 1])$ of a function $f$, which is continuous on the interval $[0,1]$ and admits a bounded analytic continuation onto the disk $K=\{z: |z-1|1\}$, the relation $\mathscr{E}_n=O[\omega_f(e^{-\sqrt{n}})]$ is valid. 
@article{MZM_1972_11_2_a0,
     author = {A. A. Gonchar},
     title = {Piecewise polynomial approximation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {129--134},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a0/}
}
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A. A. Gonchar. Piecewise polynomial approximation. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 129-134. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a0/