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Aubakirov, T. U.; Bokaev, N. A.

On a new class of function systems of Faber-Schauder type. (English. Russian original) Zbl 1213.42085

Math. Notes 82, No. 5, 575-582 (2007); translation from Mat. Zametki 82, No. 5, 643-651 (2007).
Summary: 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.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

Keywords:

Faber-Schauder function system; piecewise linear function; Vandermonde determinant; modulus of continuity; modulus of smoothness
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References:

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