Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$

“…for these spaces was constructed in ref. [4]. Moreover, for l = 2 μ , μ ≥ 0, m ≥ 0, the authors of the cited paper prove that the first m + l + 1 functions of this sequence, i.e., …”

Section: If This Space Is C M (I D ) or W M P (I D ) A Schauder Basimentioning

confidence: 92%

A convergence result for a least-squares method using Schauder bases

Palomares¹,

Pasadas²,

Ramírez³

et al. 2008

Mathematics and Computers in Simulation

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“…is orthonormal in the space L 2 [0, 1] and it forms a basis in the space V (see [1,6,9,10]). Now we define the sequence {S n (x)} ∞ n=1 of cubic splines such that S n (x k ) = 1 for x k ∈ ∆ n , k = 1, 2, .…”

Section: The Gevorkyan Problem For the Spacementioning

confidence: 99%

On a problem of Gevorkyan for the Franklin system

Wronicz¹

2016

OpMath

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Abstract. In 1870 G. Cantor proved that if limN→∞ N n=−N cne inx = 0 for every real x, wherecn = cn (n ∈ Z), then all coefficients cn are equal to zero. Later, in 1950 V.Ya. Kozlov proved that there exists a trigonometric series for which a subsequence of its partial sums converges to zero, where not all coefficients of the series are zero. In 2004 G. Gevorkyan raised the issue that if Cantor's result extends to the Franklin system. The conjecture remains open until now. In the present paper we show however that Kozlov's version remains true for Franklin's system.

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Construction of an orthonormal basis in $C^{m}(I^{d})$ and $W^{m}_{p}(I^{d})$

Cited by 62 publications

References 0 publications

Strong summability of Ciesielski–Fourier series

Strong summability of Ciesielski–Fourier series

A convergence result for a least-squares method using Schauder bases

On a problem of Gevorkyan for the Franklin system

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