Geodesic
Order of growth of the degrees of a polynomial basis of a space of continuous functions
Matematičeskie zametki, Tome 22 (1977) no. 5, pp. 711-728 
V. N. Temlyakov. Order of growth of the degrees of a polynomial basis of a space of continuous functions. Matematičeskie zametki, Tome 22 (1977) no. 5, pp. 711-728. http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a10/
@article{MZM_1977_22_5_a10,
     author = {V. N. Temlyakov},
     title = {Order of growth of the degrees of a~polynomial basis of a~space of continuous functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {711--728},
     year = {1977},
     volume = {22},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem under consideration is the one posed independently by C. Foias and I. Singer and by P. L. Ul'yanov concerning the minimal growth of the degrees $\nu_n$ of a polynomial basis $\{t_n(x)\}_0^\infty$ of a space of continuous functions. It is shown that there exist an absolute constant $C$ and a polynomial basis $\{t_n(x)\}_0^\infty$ such that $$ \nu_n\le C(n\ln^+\ln(n+1)+1),\quad n=0,1,2,\dots $$ The feasibility of the method employed is also considered.