The Fourier coefficients with respect to the Faber-Schauder system

Goryachev, A. P.

doi:10.1007/bf02102406

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1997

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Cited by 2 publications

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“…Theorem 4 for p --co was proved by Goryachev [12] directly without using Ciesielski's theorem and the proof of a theorem sim~lar to Theorem 3.…”

Section: ])mentioning

confidence: 92%

Approximation of functions of boundedp-variation by polynomials in terms of the faber-schauder system

Волосивец

1997

Math Notes

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ABSTRACT. In this paper the best polynomial approximation in terms of the system of Faber-Schauder functions in the space Cp [0, 1] is studied. The constant in the estimate of Jackson's inequality for the best approximation in the metric of Cp[0, 1] and the estimate of the modulus of continuity Wl_i/p are refined. ~0 x ~,~(t) ----2 k/2+I hn(t)dt,It is readily seen that( 1) where {hn(t)} are Haar functions (see [1, pp. 76-77]), and n, as above, is expressed as 2 k + i. As is well known, [1, p. 215], if the series n-~0

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“…Theorem 4 for p --co was proved by Goryachev [12] directly without using Ciesielski's theorem and the proof of a theorem sim~lar to Theorem 3.…”

Section: ])mentioning

confidence: 92%

Approximation of functions of boundedp-variation by polynomials in terms of the faber-schauder system

Волосивец

1997

Math Notes

View full text Add to dashboard Cite

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“…This system, consisting of continuous piecewise linear functions, is one of the simplest bases in the space of continuous functions on [0, 1]. More recently, various properties of the series expansions of functions in this system were studied by a number of authors [4]- [9].…”

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confidence: 99%