Geodesic
Orthogonal polynomial Schauder bases in~$C[-1,1]$ with optimal growth of degrees
Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 433-454

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For each $\varepsilon>0$ an orthogonal Schauder basis of algebraic polynomials $P_n$ in $C[-1,1]$ is constructed such that the degrees of the polynomials have the estimate $n(1+\varepsilon)$. This growth rate is the lowest possible. 
@article{SM_2001_192_3_a5,
     author = {M. A. Skopina},
     title = {Orthogonal polynomial {Schauder} bases in~$C[-1,1]$ with optimal growth of degrees},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {192},
     number = {3},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_3_a5/}
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M. A. Skopina. Orthogonal polynomial Schauder bases in~$C[-1,1]$ with optimal growth of degrees. Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 433-454. http://geodesic.mathdoc.fr/item/SM_2001_192_3_a5/