Geodesic
On some results and problems in the theory of bases
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 274-284 
P. L. Ul'yanov. On some results and problems in the theory of bases. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 274-284. http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a14/
@article{ZNSL_1989_170_a14,
     author = {P. L. Ul'yanov},
     title = {On some results and problems in the theory of bases},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {274--284},
     year = {1989},
     volume = {170},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The survey touches on the following three themes: (1) the order of decay of Fourier coefficients with respect to some orthogonal systems; (2) the order of approximation of functions of a given class by partial sums of orthogonal series; (3) the lowest possible order of growth of degrees of polynomials, constituting a basis of $C(0,1)$. A discussion of the present state of some unsolved problem is included and some new ones are posed.