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

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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. 
@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},
     publisher = {mathdoc},
     volume = {170},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a14/}
}
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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/