Geodesic
On a New Class of Function Systems of Faber--Schauder Type
Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 643-651

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In this paper, we introduce a new class of function systems generalizing the classical Faber–Schauder system. Under the condition that the generating sequence is bounded, we show that systems of such a class constitute bases in the space of continuous functions and prove some properties of series expansions of functions in these systems.
Keywords: Faber–Schauder function system, piecewise linear function, Vandermonde determinant, modulus of continuity, modulus of smoothness. 
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     author = {T. U. Aubakirov and N. A. Bokaev},
     title = {On a {New} {Class} of {Function} {Systems} of {Faber--Schauder} {Type}},
     journal = {Matemati\v{c}eskie zametki},
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T. U. Aubakirov; N. A. Bokaev. On a New Class of Function Systems of Faber--Schauder Type. Matematičeskie zametki, Tome 82 (2007) no. 5, pp. 643-651. http://geodesic.mathdoc.fr/item/MZM_2007_82_5_a0/