Geodesic
Composite functions and their series in the Faber--Schauder system
Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 395-415.

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We obtain both necessary conditions and sufficient conditions for the absolute convergence of the series of Fourier coefficients with respect to the Faber–Schauder system for composite functions of various classes. 
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T. N. Saburova. Composite functions and their series in the Faber--Schauder system. Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 395-415. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a4/

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