Geodesic
On series with respect to the Faber--Schauder system and with respect to the bases of the space $C[0,1]$
Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 185-195.

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In this paper we investigate the sequence of coefficients of the expansions of continuous functions with respect to normed and quasinormed bases of the space $C[0,1]$. In this connection one makes use in an essential way of the properties of the Faber–Schauder system of functions. Some adjoining questions are investigated. 
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     author = {V. G. Krotov},
     title = {On series with respect to the {Faber--Schauder} system and with respect to the bases of the space $C[0,1]$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {185--195},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a2/}
}
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V. G. Krotov. On series with respect to the Faber--Schauder system and with respect to the bases of the space $C[0,1]$. Matematičeskie zametki, Tome 14 (1973) no. 2, pp. 185-195. http://geodesic.mathdoc.fr/item/MZM_1973_14_2_a2/