We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-6, author = {Krzysztof Wo\'zniakowski}, title = {On an orthonormal polynomial basis in the space C[-1,1]}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {181-196}, zbl = {0990.46006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-6} }
Krzysztof Woźniakowski. On an orthonormal polynomial basis in the space C[-1,1]. Studia Mathematica, Tome 147 (2001) pp. 181-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-2-6/